Considering that there was talking during the games between the players, about 17 moves were made in under a minute and they were playing with expensive vintage Staunton sets, no. There is much that is far from the true chess congress, but admittedly apart from this, they didn't do such a bad job.
It is frankly disappointing as a chess player that you can only see about half of the chess board at best during most scenes, whilst most of the screen is filled with their reactions. I think the chess players who watch this will want to know more details of the actual games themselves rather than the backstory, but this is hardly surprising considering it is aimed at a broad audience.
Also, when the players talk about the moves, they say "move the queen here" and "queen takes rook" and "I can take your pawn on this square". In reality, a post-mortem analysis between two master players will go something like this " I thought I had 22. PxP and if BPxP 23. R-B1 Q-N1 with 24. Q-R5 P-R3 25. N-N5 with a strong attack and if you play 22...QPxP then I had blad de bla de bla (frantically moving around the pieces to show some variation). Then the other guy says, but if you had gone 22,PxP I'd have gone here ..etc. etc.
A lot more concrete.
But all in all, rant over... Apart from these minor problems I have with it, they didn't do a terrible job I suppose.
Of course, if you don't see the board much, even actual chess players aren't going to be able to follow a string of moves.
Myself, I ended up pausing a lot of times to try to figure out the games. (I actually thought Beth's game against the 13-year-old Girev (based on a Jakovenko game) was a Judit Polgar game -- the game I was thinking of also had the g5/h4->h5 vs g6/h6 breakthrough motif). I would have liked to see even more Easter eggs in games of other players, but considering most of the players are more or less props for Beth's triumphal procession, I can see why it didn't happen.
Don't get me wrong, I liked the show a lot, but Beth winning every game except against whoever her strongest opponent is at the moment is a flaw in the book and it remains so in the show (actually, that's not 100% true in the book, though it is in the show -- and she still has no draws at all in the book, I believe). At the very least she should have had some draws, and really the occasional draw or even loss could have made for more dramatic tension.
Yeah, adults say movies gotta have that... 
Considering that there was talking during the games between the players, about 17 moves were made in under a minute and they were playing with expensive vintage Staunton sets, no. There is much that is far from the true chess congress, but admittedly apart from this, they didn't do such a bad job.
It is frankly disappointing as a chess player that you can only see about half of the chess board at best during most scenes, whilst most of the screen is filled with their reactions. I think the chess players who watch this will want to know more details of the actual games themselves rather than the backstory, but this is hardly surprising considering it is aimed at a broad audience.
Also, when the players talk about the moves, they say "move the queen here" and "queen takes rook" and "I can take your pawn on this square". In reality, a post-mortem analysis between two master players will go something like this " I thought I had 22. PxP and if BPxP 23. R-B1 Q-N1 with 24. Q-R5 P-R3 25. N-N5 with a strong attack and if you play 22...QPxP then I had blad de bla de bla (frantically moving around the pieces to show some variation). Then the other guy says, but if you had gone 22,PxP I'd have gone here ..etc. etc.
A lot more concrete.
But all in all, rant over... Apart from these minor problems I have with it, they didn't do a terrible job I suppose.