It's worth mentioning the truly ludicrous number of positions that chess networks are trained on, usually in the billions. Which is a bit interesting, because it suggests they're not as good at generalizing from examples as human grandmasters, who might see only millions. Perhaps this isn't surprising, since LLMs are this way with language, but given the structure of chess it's be reasonable to expect they wouldn't be quite as data hungry.

My personal take is that chess isn't all that structured, really. Yes, the ruleset, pieceset, and board are small, but the tactics of the game make it chaotic – seemingly trivial differences in board state can lead to dramatically different consequences.