How we cite our quotes: (Paragraph)
Quote #1
Like most of the other Chinese children who played in the back alleys of restaurants and curio shops, I didn't think we were poor. (3)
Waverly begins without any real knowledge of the world around her. More importantly, she's "like most of the other Chinese children," meaning that there's nothing different or special about her. This changes once she finds chess—not only does she become different, her childhood starts slipping away.
Quote #2
At the end of our two-block alley was a small sandlot playground with swings and slides well-shined down the middle with use. The play area was bordered by wood-slat benches where old-country people sat cracking roasted watermelon seeds with their golden teeth and scattering the husks to an impatient gathering of gurgling pigeons. (5)
Look closely at the voice here. This isn't a little girl telling you what she sees; this is a grown-up woman looking back at her childhood. She sees details that wouldn't register with a kid, like noticing that old people are at the playground as well as children. The narrator's aware of the innocence she had as a little girl, which an actual little girl would be unaware of.
Quote #3
My brothers and I believed the bad people emerged from this door at night. (8)
Innocence and youth comes through here as an act of imagination. "Bad people" sounds like fairy tale monster here, something kind of fun and cool to be marveled at, rather than anyone really scary. The paragraphs around this one are littered with these kinds of description, showing the world through a little girl's eyes. Those descriptions change subtly as the story goes on, though, marking Waverly's maturation.