The definition thing was a joke.
But seriously, I don't know how to answer your question. Poetry is poetry no matter if it's broken sentences or broken words. Almost any form of condensed language could be considered poetry. The slang I talk, the shorcuts you might take in your everday language, using metaphors in your speech. These are all things that elevate language to poetry, good bad and ugly.
This poem in particular is a broken story. The verses are as they are because one very long sentence after another is not very pleasing to the eye. It was a stream of conciousness poem, so what came out is what came out.
Although I was just playing with the dictionary.com thing lets take another look at it.
Quote:
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Prose that resembles a poem in some respect, as in form or sound.
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Now the poem above definitely has rhythm and metre and is therefore poetry in every sense of the word even literally and emotionally. However you feel it is broken prose. But by this very definition and according to what you have said of the poem, it is indeed poetry.