I wouldn't go so far as to say that Grizzly likes action movies. At least not in the same way that Fuzzy liked Jurassic Park movies. But when he was ready to go, all the shooting and explosion attracted his interest long enough that he didn't immediately run back to the cage.
Supposedly guinea pigs are afraid of loud noises, but Grizzly just seemed curious. Or maybe he just wanted to see if McClane was going to make it.