The extended metaphor of life being compared to chess is evident throughout the story, "Rules of the Game." While Waverly is on one side of this metaphorical chessboard, her mother is on the other end. This is made clear by the last paragraph of the story:
"Her black men advanced across the plane, slowly marching to each successive level as a single unit. My white pieces screamed as they scurried and fell off the board one by one."
While Amy Tan clarifies this metaphor here, it's evident throughout the story as mother and daughter continue to battle for supremacy in a world foreign to one and native to the other.
In the first instance in which chess is mentioned, the mother calls the rules of that particular game, "This American rules. ... Every time people come out from foreign country, must know rules." In this new world, Waverly's mother suggests about moves in chess, "Better you take it, find out why yourself."
Meanwhile, Waverly has a desire to learn the rules, becoming obsessed with the pawns inability to attack. In addition, she joins an American chess tournament, which is against her mother's wishes because "They would have American rules. If I lost, I would bring shame on my family."
These contrasting desires, Waverly's to play by the written rules of America and her mother's to learn the rules for herself, put the two at odds throughout the story. They truly are opponents.