Correct me if I am misunderstanding, but it seems you are claiming that games won on time are not real "completed games", so there can never be a winner or loser in such games.
No, I am saying the winner is assigned by rules outside of the basic game of chess. You could consider it a variant, I suppose.
Why should we believe that? The players
You mean the players that are rated and part of a federation...but yes, go on...
believe that it is a real and complete game. FIDE believes that those are real and complete games. Why should we think that FIDE (or USCF or chess.com or whomever) can mandate the rules of piece movement but not any other aspects of play?
They cannot mandate the rules of piece movement. Not in any meaningful way.
Would you countenance an opponent seeing that they have made a blunder and simply change their move if you hadn't made a move yet? That "touch move" business is just a mutually-agreed convention. We regularly see complaints on chess.com forums that taking en passant is cheating. That's something else that is simply allowed by FIDE rules. I've seen children get into fights because an opponent immediately captures a newly-promoted queen because "that's not fair". And we all know that the rules of chess have changed over time, they were not brought down by Moses from Mt. Sinai on stone tablets.
What you consider to be the totality of chess--the "rules of play"--are decided upon by FIDE and other organizations to govern the play in competitions those organizations recognize.
They are not. The tournament rules are. The basic rules come across basically untouched. Touch move, clocks, recording moves...all additions to prevent never-ending games, disputes, or anything else that jeopardizes a tournament schedule or causes prize disputes.
Those same organizations decide what time controls will be used in their games; if we accept their authority as to piece movement, why should we object to their rules on time restrictions.
Nobody said anything about objecting to tournament rules in a tournament setting. That is not basic/standard chess, however.
If the governing bodies proclaim that the rules are "such and such" and the players agree, then those are the rules of those games.
Yes, those are the rules for much less than 1% of games played around the world every day (I am talking about tournament rules and games here since you seemed to be mostly talking about FIDE). You can also make the argument here that Chess.com has far more power over the rules of basic chess than FIDE...if enough people play online to the point that physical board games change their rulebooks to match, *then* when those 600 million people are all playing a new way, you can call that basic chess. It'll sure be fun when premoves are allowed OTB 
.
The players agree that they have won/lost the games should they violate those (or other) rules. The players take the ticking of the clock into account when deciding on their moves. Time controls are "in chess" for these players in these games. (Such games compose well over 99% of chess games played in the world today.)
Online chess, yes, and I won't be surprised to see chess clocks standard in boxed sets someday...but it sure won't be this decade. I also expect to small digitized stick displays that randomly chooses a Chess960 starting position to someday come standard.
If the players, the organizers, and the federations rating and certifying the results all agree that those were real and complete chess games with actual results, who am I to say them nay?
You're really pushing this hard, but it doesn't really work...in the same way that you can't tell a bunch of kids on the street that they aren't playing soccer right because they are not using FIFA rules. It's the former that drives the latter, not the other way around.
Yes, should someone challenge me to a game and then be forced to leave before they play a move I will indeed feel successful when I pocket the stake, and should I win a tournament in the manner you describe I would be disappointed to have missed out on playing some games of chess, but I will feel successful when I walk off with the trophy and prize money. That result would fall under the rubric of "financial gain"--the Old Dutch and original English meaning of "luck".
You give way too much power/credit to FIDE here. Players en masse determine how the game is played, and Hasbro or Milton Bradley ultimately have more say on how chess pieces move than FIDE does. When a parent goes out and buys that first chess/checkers combination set, the rulebook in that box is the rule book that matters. For 600 million people, not 6 million.
What do you think would happen tomorrow if FIDE said they were returning to bishops moving only 2 squares diagonally? What do you think happened to organizations that thought the Mad Queen variant of chess should not be made official? People didn't care, they liked the Mad Queen variant better. They like bishops that traverse whole diagonals better. They like pawns moving up to two squares initially better.
Also note that you are taking this outlook at a time in chess history when a single player and a chess website are within a hop, skip, and a jump of taking over the 6 million/1% game and pushing Chess960 at faster time controls as the standard mode of playing tournament chess. FIDE will be a fossilized husk if that happens and they don't follow along with what players actually decide to play. Tiktok and YouTube short videos will ultimately determine the course of chess from here, not FIDE.
Distractions can affect either or both players.
That's irrelevant to my argument.
Some playing sites are crowded, poorly lit, equipped with noisy air conditioning, etc. Should you wish, you might employ the Bobby Fischer method and simply refuse to play unless all conditions conform to your exact specifications. (Don't hold your breath waiting for tournament organizers to accede to your demands.) If it's too hot/cold/noisy/dark/crowded/whatever that environment might be considered as "part of" that specific game, but the ability to maintain one's concentration at a high level IS an important chess skill. Even if one player finds particular conditions more distracting than their opponent does it is still the players' moves that decides the issue.
What conditions I choose to allow has no bearing on whether they are part of the actual game in terms of claiming something is "in" chess.
If you consider tournament games (and presumably online games) involving clocks to be actual chess games, then failure to complete the moves within the stipulated timeframe must be considered "part of" those chess games.
That does not follow, actually. They affect chess games, and may cause premature cessation of chess games. But then again an agreed draw does the same. In a truly "played" chess game, the result is either checkmate, or draw, via lack of material or stalemate. Every other result is a tacit agreement (directly or indirectly by adding external rule constructs/clock) to stop playing the game before it is over.
One player's failure to complete the game on time results in a loss (and the opponent's win). The position of the pieces on the board has no bearing on victory/defeat (success/failure) in that game. Time management is another chess skill in timed games.
It results in a forced cessation of the game and an "assigned" loss that did not actually take place. Time management is a skill that does not apply to basic chess games, and despite your experiences, I would contend that untimed games are still a majority of games played worldwide. Chess.com claims 600+ million people play chess. FIDE has 360,000 active members. Major federations *might* add an order of magnitude to this (let's be generous and say 6 million tournament players. That's 1% of players, admittedly the most prolific ones, but they would need to play 100 games to the casual player's 1.
In rare instances, such as internet failures or strokes at the board, the players' time management skills are not the cause of clock expiration and the game's outcome. The moves made by the players have no influence on such games' outcomes.
You are right, those game were halted by external circumstances.
"Success apparently brought about by chance rather than through one's own abilities or actions" (OED) means luck.
Success *in chess* is not present in the cases you are referring to. If you meet someone at a coffee house and you agree to play a game, then they get a text before the first move and say "I have to go, emergency...sorry, I resign."...do you feel "successful" in the context of the chess game you have just technically "played"? Extend to the extreme...say you played in a tournament and every single opponent resigned before the first move. You win the tournament! (maybe there's some investigation afterwards, but...)
Did you succeed in chess? No, not one bit. You did however win the tournament, i.e. the external construct that surrounded and encapsulated your individual chess games.
How exactly do you explain who won such games, and how they did so, within the "very consistent" and "far easier to delineate" definitions you propose? Perhaps your parameters do not cover all eventualities?
They cover them nicely, I think.
A game of chess can be considered to have truly started when both players have made a legal move with a continuing intent to play out that game. It ends with checkmate, an insufficient material draw, or stalemate. Everything else is outside that game of chess. The pairings are not part of the game, hitting the clock is not part of the game, writing your moves down is not part of the game, arbiter interventions are not part of the game, the power blackout in the tourney hall is not part of the game, your opponent flipping over the chess board and walking away is not even part of the game. Tournament rules are imposed to force games to fit the time schedule and resources available. Any abnormal terminations they cause, whether agreed upon or not, are not part of the game. Your laptop falling the toilet is not part of the game. Rather it is an external event that is part of your life, the player, not the game.
Game and/or external rules like tourney rules that cover cessation of play outside of direct victory/draw conditions do so to allow for a reasonable exit from play, not to imply that your game was "successful" or completed.
Correct me if I am misunderstanding, but it seems you are claiming that games won on time are not real "completed games", so there can never be a winner or loser in such games. Why should we believe that? The players believe that it is a real and complete game. FIDE believes that those are real and complete games. Why should we think that FIDE (or USCF or chess.com or whomever) can mandate the rules of piece movement but not any other aspects of play? Would you countenance an opponent seeing that they have made a blunder and simply change their move if you hadn't made a move yet? That "touch move" business is just a mutually-agreed convention. We regularly see complaints on chess.com forums that taking en passant is cheating. That's something else that is simply allowed by FIDE rules. I've seen children get into fights because an opponent immediately captures a newly-promoted queen because "that's not fair". And we all know that the rules of chess have changed over time, they were not brought down by Moses from Mt. Sinai on stone tablets.
What you consider to be the totality of chess--the "rules of play"--are decided upon by FIDE and other organizations to govern the play in competitions those organizations recognize. Those same organizations decide what time controls will be used in their games; if we accept their authority as to piece movement, why should we object to their rules on time restrictions. If the governing bodies proclaim that the rules are "such and such" and the players agree, then those are the rules of those games. The players agree that they have won/lost the games should they violate those (or other) rules. The players take the ticking of the clock into account when deciding on their moves. Time controls are "in chess" for these players in these games. (Such games compose well over 99% of chess games played in the world today.) If the players, the organizers, and the federations rating and certifying the results all agree that those were real and complete chess games with actual results, who am I to say them nay?
Yes, should someone challenge me to a game and then be forced to leave before they play a move I will indeed feel successful when I pocket the stake, and should I win a tournament in the manner you describe I would be disappointed to have missed out on playing some games of chess, but I will feel successful when I walk off with the trophy and prize money. That result would fall under the rubric of "financial gain"--the Old Dutch and original English meaning of "luck".