It's a fake. Note the lack of expended shell casings, lack of recoil, and muffled sound. I've fired an AK and they are a lot louder than what's shown. Also note the source of the vid is the 20th Century Fox film library. The same 20th Century Fox that released their new Planet of the Apes movie about when this video went viral. My guess is this is a movie outtake from the film.
I'm no expert in primate behavior but unless the chimpanzee (not monkey) is used to loud noises, the first shot would cause most to drop the weapon and flee.