If they excessively quote the original letter in their reply, it’s not real. Nobody puts this amount of effort into a rejection when they are obviously being mocked by the sender. They would send a generic “not what we’re looking for” rejection letter at most.

This is almost certainly the case.

BUT

If I were an admissions officer and got an application like the one hinted at I’d probably put the time into a rejection like this since it’s clearly what the sender was really after. I mean, it’s clear fake, but I kind of wish it wasn’t

The problem is that the second you responded to something like that you’d be buried in copycats the next year all hoping to go viral. So you’ve made your job more difficult or burnt bridges on the way out the door.