Is the excerpt from Amy Tan's The Joy Luck Club titled "Two Kinds" considered narrative poetry, nonfiction, or a fictionalized autobiography?

“Two Kinds” is a fictional autobiography because it tells the story of the little girl Jing-mei, who doesn’t really exist.
An autobiography is a nonfiction, or true, account of a person’s life written from that person’s perspective.  A person writes an autobiography when he or she feels that her story is interesting and worthy of being told.  In this case, Jing-Mei is the daughter of a Chinese immigrant.
In this fictional autobiographical incident, Jing-Mei describes how her mother desperately tries to turn her into a prodigy.  She tries everything, hoping that her daughter will have a natural talent for something.  She doesn’t.
Waverly actually does have a talent.  She is "Chinatown's Littlest Chinese Chess Champion."  Ths makes Jing-mei jealous.  It's one thing to be compared to Shirley Temple or the kids on TV.  She doesn’t like being compared to Waverly.

And my mother squared her shoulders and bragged: "our problem worser than yours. If we ask Jing-mei wash dish, she hear nothing but music. It's like you can't stop this natural talent." And right then I was determined to put a stop to her foolish pride.

Jing-mei is not actually a musical prodigy.  Her mother is exaggerating and doesn’t realize the true state of her daughter's skill.  When she finds out that Jing-mei has been lying to her, she is surprised.  Jing-mei seems almost as surprised as everyone else that she does so badly at her recital.  She was daydreaming so much that she never practiced.