I think it's because Waverly had seen her mother as a chess opponent. In the story, In the Rules of the Game, Waverly's life is like a chess competition. She wanted to appease her mother's expectations and at the same time tries to live like an average kid. However, her success made her stuck in the game. Thus, her life started to revolve around chess. She can no longer go out like any other kids, all she does is practice and play chess.