Is about subjective knowledge, not objective.

So entropy is not related to the number of remaining legal states.

If I know the seed of a PRNG, the entropy of the numbers it generates is zero for me. If I don't know the seed, it has very high entropy.

https://www.quantamagazine.org/what-is-entropy-a-measure-of-...

Sure. Lots of games result in a reduction in game state entropy as the game progresses. Many card games could be described as unnecessarily complicated ways to sort a deck, as an example. When analyzing games wrt the Second Law, consider that "the system" is not simply the current game state, but should at least include captured pieces and human choices.