I’ve now seen a few episodes, and I have a few comments on the chess:
1. No player, including Magnus Carlsen, can become that good that quickly, without a lot of learning and losing along the way.
2. They show the players moving too fast, though for dramatic reasons this is easy enough to understand.
3. The Sicilian was indeed very popular in 1963, but not quite that popular.
4. It captures the feel of earlier U.S. chess tournaments very well, noting that my own participation came later but things didn’t change much.
5. At the time the Rossolimo was in fact an unusual response to the Sicilian, though it is not now. The show got this right (the protagonist claims she was very surprised by 3.Bb5) — don’t be fooled by the subsequent evolution of the game.
Dramatically, I would say it is “decent and watchable,” and the clothes and hotel scenes are good. The characterization of the mother does not feel entirely consistent. There is an underlying autism theme, mostly handled well, though mainstream reviewers seem to be thrown off the scent by the woman’s charm and good looks. I will let you know if I have further observations.