Throughout the novel, Waverly struggles to free herself from the power her mother has over her, and the chapter "The Rules of the Game" does a wonderful job explaining the origins of this.  Waverly becomes a chess champion, but then eventually blows up at her mother for embarrassing her.  When Waverly confronts her mother, she threatens to never play chess again, but Lindo, Waverly's mom, just turns a cold shoulder.  When Waverly eventually chooses to play again, Lindo tells her it's not that easy.

The symbolism between their relationship and the game of chess is quite apparent: Waverly has the ability to beat the best of the best, but once her mother gets inside her head, she begins to doubt herself.  Trying to avoid her mother's ridicule is like trying to win a mental chess match; hence, at the end of the chapter we get the "imaginary chess game" where her mother is symbolically sitting across from her, winning this game of inner strength.

Why does Waverly get angry with her mother in "Rules of the Game"?

Although Waverly's mother is proud of her daughter's success, she upsets Waverly by critiquing her chess matches, constantly hovering over her shoulder while she practices, and showing her off at the local shops on Saturdays. Waverly's mother is depicted as an overbearing parent who wants what is best for her children but does not subscribe to the American values of independence and individual achievement. Having immigrated to the US from China, Waverly's mother values family and communal honor. Waverly resents her mother's outlook on life and desires autonomy and independence.

Waverly wishes to embrace her individual success and distance herself from her mother. As she continues to win tournaments and gain recognition as a chess prodigy, her mother makes her visit the local shops with her on Saturdays. During these trips, Waverly's mother introduces her daughter to everyone they meet. Waverly views this task as an annoying chore and is irritated by the way her mother seems to be bragging about Waverly's abilities. One Saturday, she expresses her frustration by telling her mother,

I wish you wouldn't do that, telling everybody I'm your daughter. ... Why do you have to use me to show off? If you want to show off, then why don't you learn to play chess?

Waverly's comments anger her mother, and Waverly runs off to hide in an alley. Later that night, she returns home and is shunned by her mother and family. As she lies on her bed in the dark, Waverly imagines herself playing chess against her mother and floating alone into the night sky to plot her "next move."