Nona Gaprindashvili was one of the best female chess players ever. Once the Polgar sisters managed to play in the higher levels of "mens'" chess and had a lot of success women came to be accepted everywhere and some have had more impressive achievements and higher ratings than she did, but this is partly because they got to face tougher competition throughout their careers and thereby improved their game.
"The Queen's Gambit" quote definitely points out that she was the world champion, but even so didn't get to play men. This is more of an indictment of the old system of top-level international chess than a slander of her.
Also, Gaprindashvili is 80 years old (unlikely to "learn more as she gets older") and has been retired for years, so her career has not been detrimentally affected financially, leaving no grounds for monetary compensation.
What makes you think the film brought her any financial advantage? How would that have worked? I guarantee you she’s not getting rich as a chess player. Even if she did gain some financial advantage, it wouldn’t mean she wasn’t defamed (though it might have some bearing on the amount of the award).
Well that creates a big problem for her side then. The burden is actually on her side. She's the plaintiff. She has to prove there were damages. I believe the claim is lost income from chess tournaments as a result of this so called "defamation". So lets see the numbers. Has she been making more, or less, since the Queens Gambit came out? Assuming that she has played in the roughly the same amount of tournaments per time period before and after the show aired.
As for getting in touch with Netflix or anyone else associated with the show it seems reasonable that if the general public knew about it being made, and the chess community in particular knew it was being made, it stands to reason Nona would probably know about it too. Unless she lives somewhere where there is no TV, no internet, no cable, no newspaper, and no access to the outside world, and no means to access the outside world.
I'm just saying it's what I would have done. If there was a book written that had my name mentioned, and then I find out that book was being made into a movie, I would definitely take steps to find out more about the movie. In particular what I could do to maximize my exposure. Unless she lives a very, very private life and didn't want any exposure. But then again, if she's that private, why would she be a professional chess player where pictures are taken and people say things about her?