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.
