I think what also reinforces this cycle is external and internal(!) stereotypes.

Additionally, because you have fewer strong female players, and since they segregate the game, you therefore also have fewer strong female teachers and role models.

There is also a very strange dynamic between kids and teens starting in elementary school where the boys often drive out the girls from specific activities. It's only anecdotal but I've seen it twice here in my neighborhood. In the school and in the community center a higher ranked chess player offeres free courses to teach the kids chess.

None of the girls stay when they are offered a more friendly environment like the dance class. Because you will always have a group of boys socialised to be more aggressive (pulling hair, being ultra competitive, etc.) and girls being socialised to rather avoid conflict. I know many boys also don't like this atmosphere but they will be more like "I need to be more like the other boys since I am a boy" while the girls we be like "I don't fit in here since I am a girl".

Sorry for the rant.