Something I have a mild interest in, from an anthropological perspective, is the way in which people tend to naturally role play during any sort of game scenario. (By "people", I mean irrespective of whether they have any experience with role playing games or even know what they are.) You get it a lot with games like Diplomacy and Risk of course - people begin to take on airs and behave in a self-consciously "ruler"-ish sort of a way (usually with their tongues firmly planted in their cheeks), or make threats to one another and talk with funny accents. I'm sure you've all experienced this.
But it also happens with games which are more abstract, like, say, Monopoly and even Snakes and Ladders - any sort of leisure pursuit, I suppose, which requires some level of investment in a character, counter, or other physical representation of some kind. (You can't really imagine it with a genuinely abstract game like Go, Backgammon or Poker...) Immediately the little toy iron or piece of plastic that acts as your avatar takes on a kind of personality of its own, and suddenly you feel as if you really are travelling around an early 20th Century London buying houses on Regent Street or climbing up a ladder to beat your spouse in a race to the prize.
Given the historical connections between role playing and wargaming, we shouldn't be surprised to discover that wargames elicit the urge to role play very readily. This is something I've noticed a lot of during my career as a Steel Panthers: World at War PBEM player. Not content to merely trade insults or commentary on battles as they develop, I've discovered that most opponents very readily engage in fantastical accounts in which they are a battalion commander on the Eastern Front (or wherever), communicating with their troops and often coming up with highly detailed and entertaining fictional After Action Reports of their encounters. In their email exchanges they pretend to be SS or NKVD officers issuing humorous, over-the-top commands to take no prisoners, or British majors twiddling moustaches and swilling port. The roots of our hobby are very clear in these exchanges; the gap between pretending to be a Red Army colonel advocating death for those who retreat, and between pretending to be a Red Army colonel on a secret mission with a close group of comrades is very small. The only thing separating the two is, in the end, scale and rules.
In light of this one begins to suspect that the development of role playing games was inevitable once wargames became popular. I'm reminded of that old saying that, given the achievements of Newton, Einstein and Da Vinci, you would choose the latter as more important, because somebody somewhere would have eventually made the discoveries of the former two whereas the latter's were by definition unique. In a similar way, though Gygax and Arneson et al have to be commended for their creations, somebody else in the wargaming community, given the nature of gaming in general and wargaming in particular, would likely have come up with them sooner or later. Though obviously in a very different form.