The whole story is a metaphor.
Waverly's mother taught her the art of invisible strength. This art was to win arguments and respect from others. Later Waverly would understand that this art could be used in a different area of her life - playing chess. As she did this, she excelled in chess to the point of gaining national recognition.
This fact made her mother very proud. As they would go to the market, Waverly's mother would boast to other people that her daughter was a chess champion. This extra attention did not settle well with Waverly. So, she objected and confronted her mother. After one altercation, she ran away. When Waverly came home, she realized that she and her mother were locked in a struggle. It was a game of chess. It was her move, what would she do? She lay in her bed and pondered.
From this perspective, the whole story is metaphor. Life is a game of chess to win respect. Waverly's relationship with her mother is also a game of chess.
Here is how the story ends:
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. As her men drew closer to my edge, I felt myself growing light. I rose up into the air and flew out the window. Higher and higher, above the alley, over the tops of tiled roofs, where I was gathered up by the wind and pushed up toward the night sky until everything below me disappeared and I was alone. I closed my eyes and pondered my next move.