As the first chapter where Waverly is introduced to us demonstrates, one key aspect of Waverly and her relationship with her mother is the chess game that acts as a powerful symbol of the conflict between them as Waverly grows up and tries to find her independence and break free from her mother's hold over her. This helps us to understand the way in which chess playing acts as a powerful metaphor throughout her narrative. Consider the following example from the chapter you have identified:
And she was the queen, able to move in all directions, relentless in her pursuit, always able to find my weakest spots.
Waverly here uses this metaphor to describe how she feels persecuted and pursued by her mother, and how she also feels curiously vulnerable, as if she were a pawn being pursued by a chess piece that is much more powerful and mobile than herself.