The fact that playing a game otb would eliminate the chances of internet connection interruptions couldn't determine the winner does not mean that such things don't happen in online play.
That instances of games being decided by factors other than the players' moves or poor time management are very rare does not mean that such occurrences are non-existent.

Wins and losses are essential features of chess. Whether or not you wish to consider them "in game factors" (your term, not mine) all chess players think winning/losing is an essential part of the game. Wins by time forfeit, resignation,, expulsion of a contestant for cheating or other unsanctioned behavior, or checkmate all show up as "1" on the scoreboard.
So sometimes a player achieves success "by chance, rather than through one's own actions or abilities". The win has been recorded no matter what the cause. Success was obtained through luck. If luck was not involved, how are such games won/lost?
I understand that you are saying that such success isn't envisioned in the idea of the game, but if we wish to be able to play chess in the actual world we must accept that reality doesn't always conform to our ideals.
We have been discussing fundamentals of game related objects and relevant practical examples to unpack and test what we consider 'in game factors'.. now it seems like youre zooming out and reverting back to a sort of high level slogan like argument where we originally kicked off from.. Which is unfortunate because while it sounds reasonable, it doesnt offer enough reasoning to conclude the answer to the question at hand.. unpacking the fundamentals is necessary for such progress so leaving them insufficiently addressed and going back is indeed just causing regression in the discussion.
The high level argument you bring forward is probably impossible to sufficiently address at that level and in short. If an 'in game factor' ie something that is considered a part of the game, e.g. a player (doesnt equal human by the way but any force that is capable of playing the game).. is influenced in a manner that in turn influences the game result.. or in a manner that disrupts the game completely.. it doesnt logically follow that the particular source of influence in question must be an in game factor itself. Potential influence on the result is one of the symptoms of being an in game factor but whether or not its enough to define an 'in game factor', it has to be unpacked for some logical scrutiny and testing... which we were doing. And I have proposed that a more logical definition of an in game factor would involve a direct relationship with game mechanics and principles. It is not a premise but a conclusion from testable scenarios and logical discussion.