I wouldn't really classify that as a poem either, not to detract from its artistic merit, but it's essentially prose. Not that I would go by any particular set of rules, as I think there's a lot of grey, but broadly I would agree with this in terms of what it says about structure (I disagree with it on expressiveness and language). I guess it's like reading out the lyrics of a song and calling it singing. It's not. You could have semi-singing forms, such as chants-verging-on-plainsong, but O'Hara's work isn't even that. I'll allow him the first five lines at a stretch but past that, when he gets to multi sentence paragraphs, that's 100% prose.
istara, are you aware of prose poetry? Some of the most well known poets including O'Hara (who, by the way, was the "New York School" poet) have written entire books of poetry in prose. Many people who are not involved with poetry seem to think that if something is prose, it is automatically then not poetry. This in turn contributes to the incorrect perception that poetry is devoid of meaning and relies solely on the reader to impart meaning, a.k.a. "poetry can be like, anything, man". Poetry is not dependent on structure and though poems can be narrative (and many are) that does not mean that they are stories. Part of the distinction is in intent. To get a sense of prose poetry as written by a contemporary poet, you might check out James Tate's Return to the City of White Donkeys.
If you want to class that as poetry, then fair enough. Everyone can make their own definitions. "Poetry" as a concept can be applied in abstract ways to many things. But poetry-as-in-poem: that doesn't wash for me. If you are deliberately not using any of the structural conventions that differentiate poetry and prose, why you need to call it poetry?
Don't confuse something you don't understand with sophistry. Painting a house is not "creating a painting" unless the house is used as a canvas to create art. In other words, all squares are rectangles, but not all rectangles are squares. Furthermore, what you are judging as "not poetry" is in this case, considered to be poetry by the poets (O'Hara and Tate), academics (including Tate, who is both a prize-winning poet and a professor of poetry at some of the best regarded poetry programs in America) and the publishers (who have published some of the most influential and beloved poetry of the era). So if it doesn't "wash" with you because you have an idea of what poetry "should be" though you don't seem to be well-versed in the subject, perhaps you might be well served to search out some of the many available articles in academic and literary journals to try to understand why it does "wash" with people who write, teach, publish and actually read poetry. Understand that poetic traditions across cultures vary greatly and to judge one culture's poetry against a foreign metric, is simply unworkable.
I'm not saying it's sophistry, nor that I don't understand the arguments they may make to claim it to be poetry. I am simply saying that from what I personally judge to be poetry, it is not poetry. I also note: There are several things that have won the Turner Prize that are considered art by a huge range of informed people within the field but I do not think they are art. They are interesting concepts, but they are not art to me. You can make assumptions all you like about my ignorance but even if I was the most ignorant person in the world (which actually I'm not on this issue, but that's by the by) it would still be my right to hold the view that this is not poetry. If others want to call it such, and if venerable professors of poetry want to call it such, and if readers want to call it such, good for them. I don't share their view. I also suspect if I cast around widely enough I would find plenty of other venerable people who would share my view. (T S Eliot, for one). That's why it's a view, not a fact.Prose poetry should be considered as neither primarily poetry nor prose but is essentially a hybrid or fusion of the two, and accounted a separate genre altogether.
You argued on the basis of convention. Convention changes over time to include new things, which I am certain Eliot would also agree with, especially as Eliot's own work did not follow the conventions of the day. When art becomes tradition, is it still art? Maybe, but part of art is exploring the new. The emphasis on narrative poems as well as the emergence of prose poems and micro or flash fiction might well indicate the creation of another genre in time, but I don't think anything so cohesive has yet coalesced.
What about slam poetry in that case, mostly built off beat poetry. Long, rambling verses that grow based on flow more than structure? Trying to define 'poetry' is hard enough, let alone trying to define it from a structure standpoint, and that really goes for any art form. Creating tidy limitations will inevitably be broken down as a new perspective comes in. What is 'poetry'? What is 'music'? What is 'art'? I don't know that creating a line between poetic pieces, such as Tom Waits Nighthawks at the Diner, for example, and strict poetry itself benefits anyone or anything in the medium itself. Obviously there's a distinction between poetry and prose, but I don't think there isn't overlap either. That O'Hara piece isn't even a disputed poem these days, but was when it came out. People even cast doubt on Ginsberg's Howl as a poem. Subjectivity is a fascinating subject.