I doubt you can boil it down to any one specific factor. Initial exclusivity (to universities, where FB is particularly useful), unlimited photo sharing, games, etc. are all going to drive adoption by different (overlapping to some extent) groups of people.
Ten years ago, when FB was gaining steam, everyone in my workplace was talking about Mafia Wars. Whatever other actions propelled FB, games were certainly a component.
I don't know how many users signed up only for games, but in my circles it was a minority that used it mostly for gaming, though it really was a big part if it.
