I don't think the idea is to see how well you can spot a farce, (regarding the poetry/parody quiz) but rather to prove the school of spoofs right in that some of this poetry is well, bologne? Don't you think?
I think the point is not so much about how well one can identify good or bad art. It seems more of a commentary and criticism on the snobbery exhibited by those who fancy themselves connoisseurs of fine art by seeking to show they all are full of crap. Perhaps they are.
The answer supplied to your query at the reverent.org website seems to confirm that it was the elitism fueling the rise of so many "schools" of poetry that was being parodied and not individual poems or poets. As to whether a parody should be humorous, I think so, else the parody would be as tediously boring as some awful, long-winded prose critique.