There are many themes in the short story, "The Rules of the Game."
First, it is important to note that Waverly Jong is a Chinese-American girl. More to the point, she is from an immigrant family. So, there is a clash of cultures. Her Chinese culture is more oriented towards the family and community, whereas her American upbringing is more individualistic. She is, therefore, trying to find her way.
Second, there is also the rivalry between her bothers. We can say that sibling rivalry exists. In addition, since she is a girl and her brothers are boys, there is also a battle among the sexes. In some ways, Waverly intimates this, as she was able to play chess with them by coaxing her brothers with candy. In other words, she had to be cunning in order to get her way.
Finally, the most dominant theme is the rivalry and struggle between mother and daughter. Waverly wants to break free and be her own person, but her mother resists. At the end of the story, the conflict escalates, and Waverly ponders what she should do.