Blizzard not only let them use, but I believe they even helped them.
http://en.wikipedia.org/wiki/Make_love_not_warcraft

 

That's pretty cool!
Looks like they also used some quotes from the Leroy Jenkins video

 

Blizzard did help a lot in the making of the episode. they created a ton of custom animations and all of the filming in-game was not done on live servers but in private Blizzard-only test servers. I am mildy aquianted with the designer that works at blizzard whose job for the past few weeks was helping South Park with this episode