How, then, would you distinguish between prose and poetry, while being consistent with your assessment of those two poems?

The only features that give any clue Gorman's writing is meant to be a poem (when you put it in paragraph form) are the random rhymes and the rhythm. But those formal features are no longer regarded as essential to poetry. Indeed, they're old-fashioned.

Whereas if someone wrote paragraphs in that laboured way I wrote in the poem, describing a brain with original images instead of just saying "brain," you'd surely think that prose would be highly unusual. That's because the prose would be poetic, no? As in, more creative than the average prose. By that standard, Gorman's poem doesn't come off as poetic.