The chess games played in the series to the extent that they can be followed have been analyzed on YouTube. Most of them are based on real games played by Grandmasters. I recognized the final position from a famous Paul Morphy game from around 1859. One difference is that Paul Morphy played the brilliant game while blindfolded.
At one point in the show someone presents Beth Harmon with a 3 move chess problem. This problem appeared online somewhere. This particular problem should have been at least somewhat difficult, but I just happened to pick up on the answer within a few seconds.
Composed chess problems have a rule where the first move can't be a capture or a check. This sometimes means that the losing side is placed in zugzwang, which means that it is unfavorable for him to have to make a move. These problems are much more subtle than positions from real games.
Because these problems are often very difficult, I have a technique where I imagine a couple of moves for the losing side and then given those moves I look for a way to win. If I can't solve it then I know that the solution involves preventing those moves from happening.
I have some thoughts on what the possible symbolism of the ending of the show might mean. I would like to discuss it with somebody who has seen it.