The big difference is that in Chinese, the written form of the poem is clear and unambiguous (if not terribly sensible), whereas in English that makes no sense without a detailed explanation of how you're supposed to parse it.
Yeah, I doubt anybody in real life (as opposed in an academic setting, or after having read this) ever actually knew more than 2 or 3 of those contrived definitions of buffalo (basically the animal and the place) needed to make this work...
There are only 3 meanings used in that sentence.
Looked it up and you're right, I remembered it as having more, but those (what was more) where the roles played by each of the repetitions of the 3 basic meanings (noun, verb, relative clause, verb phrase -- "buffalo", "buffaloed" (bullied), "from Buffalo", "to buffalo", "that's a bufallo (bully)", etc)