Yes, animals do need intellectual stimulation to stay happy and healthy. That's why you see things like a particularly popular series of photos showing apples frozen in a block of ice given to a polar bear. For large cats the handlers often hide food throughout the enclosure, or put it in hard to reach places. Even then, it's only a substitute for real hunting.

Something like a snake might not have the capacity to figure out a puzzle or do anything outside of it's normal behavioral patterns. A mammalian brain is much more complex and adaptable than a reptilian brain. The snake therefore cannot get such stimulation from alternate activities. The same argument might, however, be used to say that the simplicity of the reptilian brain suggests that a snake needs no such stimulation in the first place.

It's hardly a cut and dry situation, and it's important to realize that it's highly polarized as well. Be wary of both sides in this debate.