McCauley was using religion in a very broad sense, he pointed out it didn't necessarily mean belief in a supreme being or beings. As I mentioned, he was even willing to consider merely the ritual burial of dead to be "religious". Also, he was definitely drawing a distinction between religious activity ("natural") and theology. He pointed out that while religious rituals do have meaning, often the participants are unaware of the meaning or not thinking about it while participating in the ritual.
I felt one of the bigger points he was making about "religion" was this aspect of focusing on agents causing things as an explanation. He said when learning about the world, it's important for small children to discriminate between agents (things with a motive that cause events) and non-agents (things like chairs and pizza). So part of his definition of religion was the concept of ascribing events to super-natural agents.

As far as what religion means to me, that's another topic, but I'll definitely go along with McCauley's definition for now, as far as it takes us.

--Eric