What can you call a joke, pun, or anything funny that likely needs intelligence to get?
All I can come up with is intellectual jokes; is there another word for this? A one-word answer would be great.
I would call that cerebral humor. Dennis Miller is fairly cerebral.
Merriam Webster (above link) even uses that as an example usage of the word.
He's a very cerebral comedian.
Consider highbrow humor. Oxford Online defines highbrow as
Scholarly or rarefied in taste
a natural aptitude for using words and ideas in a quick and inventive way to create humour: -ODE
Witty jokes usually need some intelligence to get (and make for that matter).