We don't mean poetic in the sense that the story rhymes or that it's structured in stanzas. We mean poetic in the sense that Baldwin's writing is lyrical and beautiful. Check out this passage:
As the singing filled the air the watching, listening faces underwent a change, the eyes focusing on within; the music seemed to soothe a poison out of them; and time seemed, nearly, to fall away from the sullen, belligerent, battered faces, as though they were fleeing back to their first condition, while dreaming of their last. (179)
There is something almost musical about the way Baldwin puts his sentences together here: he's somehow able to make this description of the neighborhood's downtrodden residents really lovely.
And there's something else going on with Baldwin's style as well. The fact that his writing seems musical is certainly appropriate for a story that features music as one of its central themes. In a way Baldwin's style mirrors his subject matter, and it sort of preps us and prompts us to read a certain way. There's a definite cadence (like a musical beat) to his writing and he shows us how technique and plot can work together to create a narrative.