A game could be solved even if its state space was too large to enumerate, for example if you could show that there was some latent structure that let you prove things about large parts of the state space without completely exploring it.

This is, for example, why we have a concrete number for the number of legal go positions even though there are far too many to enumerate. https://en.wikipedia.org/wiki/Go_and_mathematics#Legal_posit...

The rules of chess are so irregular that it seems likely that any latent structure would be tremendously complex, but you never know what some clever new analysis technique will do.