I’m not sure if there are any rules per se that dictate what a poem truly is.
It used to be that a good poem had to rhyme. Today, I think that holds more true of a song lyric than a poem. Yes, I think it is still wonderful to read a well- (and organically) rhymed poem, but often as not, I do not look for, nor do I miss rhymes (or obvious rhymes) if they are no longer there.
So many incredibly fine poets placed no emphasis whatever on meter and rhyme, and all emphasis on the breath of the whispered.