By that definition, the entropy of a game of chess decreases with time because as the game moves on there are less possible legal states. Did I get that right?
Low entropy in chess means effective prediction of future moves, which is far less useful than dedicating equivalent effort to choosing a good next move for ourselves.
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.
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-...