Chess is its rules. Same rules+differrent pieces=same game. Different rules+same pieces=different game.

This isn't strictly speaking true. Note that there have many different games called chess. For example, pawns being able to move 2 squares on their first move, en passant, castling, and the queen being able to move as she can, are all recent innovations. But let's put that aside and explore your analogy. If there's one thing called "morality" then I fail to see how that isn't but one game among many. You seem to be treating morality like chess (in that there's an objective thing that is or is not chess) but are then bringing along for the particular game called "morality" all sorts of assumptions about whether or not people should play it or expect to play it. This seems akin to asserting that because there's only one objective game called "chess" that entities "should" play it.