This seems impossible. If you started with chess pieces and a chessboard or even a go board and go pieces, it is absolutely impossible to reconstruct the game as they’re currently played.
Whichis is fair and good, bc nobody would expect you to rebuild the actual rules of chess from the board alone.
However it would still be useful if archeologists used the board to figure out some games similar to checkers, or go; or if they also have the pieces they could guess it was a combat game like Shogi. Any of those would give you insight about the kinds of leisure that people may get from that board.
