Now some idiot is going to say "it isn't about winning and losing"! 
Luck in Chess
If you hang your Q for nothing and are ready to resign when your opponent takes it but ..... he doesnt notice it and makes another move instead and you go on to win the game then you were LUCKY ! If you are 4 moves away from being mated and suddenly your opponent has the " shits" and must rush off to the toilet and doesnt get back to the game until his time runs out and he loses you were LUCKY ! Luck does exist in chess , both good and bad whether people recognize it or not .
When the word "luck" is applied to a game, don't most people mean that something "improbable" happened? I don't understand the difficulty here. The guy in the video is saying that it's improbable that a 2800 rated player will lose to a 2400 player, but statistically it will happen. But, I think he loses people comparing chess to backgammon. Because the role of dice is random, it's much more likely that a novice could beat the best player in the world at bacgammon, then a novice beating the best chess player. That's where the video is wack imo. BTW, I have not read all of the posts, so apologies if we've been over this.
Not much luck in chess
Every time I win I feel lucky - my opponent was not obliged to make all those mistakes, but nevertheless he made them.
"It's common for people to find arguments against their beliefs to be "uninteresting"."
It's common for people to think the almost tautological statement "if luck exists in everything, then luck exists in chess," to be uninteresting. But, by all means, your interpretation is so much more plausible :)
Perhaps we define interesting differently. I mean, I would think you would agree that the above statement would be uninteresting. So it might not be so unbelievable that I find it more interesting to find the consequences of stipulating determinism. I mean, I won't find myself guilty for finding such an endeavor to be interesting, but, sure, you don't have to find that interesting if you don't want to. For what it's worth, we do not seem to be in disagreement about the consequences of indeterminism being true regarding the OP's question.
"Are you suggesting that it isn't luck if I happened to choose at random a line to study last night and, today, my opponent happens to play it, out of the many hundreds he could have chosen?"
Why does this have to be luck? It doesn't make your actions on the board any less legitimate or "yours." Yes, your opponent could have chosen hundreds of lines. And he chose this one. He then loses as a result of his choice. It's not a revelation. I mean, the way humans behave, we'll say things like "just so happened" for just about anything. Is the quality of luck defined as "having the ability to make humans think something "just so happened" to occur and then being bitter or happy about it?" Ok, then everything is luck, determinist or not. I just think it's kind of a weird, human-dependant definition of luck. And maybe not an effective one; it's almost like the statement "everything exists." It would be true, but wouldn't tell us much about what makes each game (poker, chess, etc.) different from another.
So I don't know I guess that's the thing for me. It's not that there can't be luck in chess, it's just that people freak out when there's something they can't predict, and so they then start thinking moves are made randomly. I don't exactly freak out when I take a game of skill, and then things I didn't predict start happening. Maybe that does mean there is luck, but I'm not one to jump to conclusions all the time and say "you're really stupid for not assuming there is luck there when really it could just be something that looked like luck but has a different nature to it compared to slots."
So I mean, sure, you can't predict what your opponent will do. But I'm not going to be obnoxious about that and then start looking for luck in everything, saying "oh I didn't know this move was good," "oh no this person obviously didn't know his move was good, he must have been lucky," as it mischaracterizes what is really going on. Yeah, skill and uncertainty run into each other when you don't have a lot of skill.
I'm not going to just give up on the term skill just because we start not knowing things. Because I'm not an inflexible person. I might instead think, well, maybe this isn't as it appears. Maybe uncertainty and skill aren't as inconsistent as they appear on the surface. And maybe they are, but I'm going to come to that conclusion by digging deep into the issue, not by making huge assumptions. I'm not going to blame myself for that policy.
I don't know, it's this same kind of presumptuous attitude that can make people unnecessarily hostile in political situations. It's like if someone said, oh shit, you're pro-choice, you're killing things, you're a murderer and you're too stupid to know that. Well, no, you're only looking at isolated aspects of the issue; that's why you think it's so simple. Unfortunately that results in people who probably don't like killing things being called murderers. Sure does escalate fast.
"It's common for people to find arguments against their beliefs to be "uninteresting"."
And for the record, I find indeterminism to be an extremely interesting view. I was fascinated by our discussion and your ideas, which is kind of why I, well, said so, in that thread. Oh well, people who want to assume the worst about you will just ignore those comments and see things through their own lens. I'll just say that I don't think people should do that, but ok, you have the final say in what you do :)
Now some idiot is going to say "it isn't about winning and losing"!
It isn't about winning and losing. Of course putting in an effort to win debates is good, since that releases the most challenging ideas. But no, I don't consider a "loss" a true loss at all. In fact losing a debate usually implies learning a lot of new ideas compared to previously.
Not much luck in chess
Every time I win I feel lucky - my opponent was not obliged to make all those mistakes, but nevertheless he made them.
Your "feeling" tells you nothing about what made your moves better than your opponent's moves.
If you hang your Q for nothing and are ready to resign when your opponent takes it but ..... he doesnt notice it and makes another move instead and you go on to win the game then you were LUCKY ! If you are 4 moves away from being mated and suddenly your opponent has the " shits" and must rush off to the toilet and doesnt get back to the game until his time runs out and he loses you were LUCKY ! Luck does exist in chess , both good and bad whether people recognize it or not .
Well another way to put it is that you simply beat your opponent. You and your opponent have to find a way to make good moves and not lose on time; you did, he didn't. Sure... the reason for a win can be different every game you play; in fact it is. It could be because of a passed pawn, kingside attack, or, sure, your opponent taking too much time in the bathroom... I don't know, be healthier next time or hold it in.
Maybe his moves were worse than his opponent's ... except for the last one!?
But moves can be weighted differently. Playing 30 good moves is great, but if in doing so you don't check for your queen hanging that's not really good chess. If you incorporate making sure your queen is not hanging then it can become good chess. So yeah, you pretty much played like a beginner if you hang your queen, even if you played GM like moves for much of the game.
That doesn't mean you're a beginner necessarily, as long as you are able to keep that queen blunder one in a million rare. But yeah, that one "rare" time you blundered your queen, it was still you playing -- you brought your same mind there, but you didn't check or something... the fact that you would check most of the time in most situations doesn't make it any less "your" decision than any other decision you make. Even if it's variance, it's variance of your own skill. Not any objective variance around you.
Anyway, there's a general tendency to ignore the strong arguments and concentrate on weak ones. Are you suggesting that it isn't luck if I happened to choose at random a line to study last night and, today, my opponent happens to play it, out of the many hundreds he could have chosen? If anyone can counter that argument effectively, they win. Otherwise, they seem to lose.