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.

Prose poem:

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.

Lyrical Vignette:

the expression of the writer's emotions in an imaginative and beautiful way in a brief evocative...

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