As is almost always the case with Whitman, this poem is written in free verse. That means that it doesn’t rhyme, and there’s no set rhythm or meter. This form of poetry was pretty controversial at the time, and for some people, it still is. The big question is: if this doesn’t rhyme or use meter, why is it a poem? Is it just a series of sentences broken up into shorter lines?
Now, there are elements here which fit our definition of poetic style. Repetition is a key one. Whitman repeats words like "filament" in a way which draws attention to their sounds. This technique is pretty different from the ones which we find in novels, for example. It is an open and personal question, though. Does this piece fit with your idea about what a poem ought to be?