According to eNotes, it is a short story. I think it tries to avoid classification. Many critics call "Girl" prose poetry or a lyrical vignette.
Work in prose that has some of the technical or literary qualities of poetry (such as regular rhythm, definitely patterned structure, or emotional or imaginative heightening) but that is set on a page as prose.
the expression of the writer's emotions in an imaginative and beautiful way in a brief evocative description, account, or episode.
I have seen the work 'Girl' by Jamaica Kincaid described in different places both as a poem and as a short story, so I guess it's down to individual opinion although critics usually tend to be able to unite on elements such as this. Different people bring different sets of experiences to each piece of writing and that affects how the piece is interpreted.
To me, the work is more like a poem because although writers experiment with brave innovations nowadays, in the style of flash fiction for example, most 'stories' -however short -have a narrative or storyline that is very clearly defined running through them. This piece is very visual, full of vivid decriptions and paints an overall picture rather than telling a story. The punctuation and run-on lines are poetic and adventurous and the non-stop list of demands makes it difficult to read as a story although the modern technique of micro-fiction and short fiction is changing all that.