The chess was fairly realistic EXCEPT
There were surprisingly realistic elements to the chess, but the one canard always seen in movies about chess was unfortunately present here as well: games playing through to checkmate. In real life, high level and even medium level players (meaning just plain amateurs who don't play tournaments but play reasonably well with their friends) can see when their position is hopeless, and they resign the game rather than playing it out. And if a game is played out for some reason (as when playing against a computer that won't resign), it will usually end with getting a pawn across and then checkmating a lone king with a mostly empty board.
The argument I suppose filmmakers would make is that casual watchers expect to see checkmates. But do people really watch slow-moving French dramas about chess without having a modicum of understanding of the game? And is it really so much less dramatic to show the losing player wilting under the pressure, frustrated, as he knocks over his king (signifying that he resigns)? I don't think so.
Now, another realistic element of chess is that between strong players, many or even most games are drawn (tied). THAT I can understand not showing repeatedly, although one or two quick appearances of draws would have been nice.