Statistically speaking, DF players are not normal.
The majority of humans are not gamers. Of the gamers, the majority of them play only mobile games. Of those who have a gaming device other than a phone, a significant number only play on consoles. Of the PC gamers, a significant fraction (quite probably a majority) play only very simple games (Minesweeper, solitaire, PopCap-style games such as Bejeweled, and so on). Of the remaining "serious PC gamers", a significant fraction only or primarily plays "action" games (FPS, RTS, etc.), and a different (although frequently overlapping) significant fraction only plays PvP games.
That leaves anyone who plays *any* sort of turn-based PC strategy game against/with the computer as a fraction of a fraction of a fraction of a small fraction of a small fraction.
Within that, you have the people who only play games which can be completed within a single session of a few hours, people who only play games with elaborate eye and ear candy (graphics and sound beyond what is needed to convey the elements of play), people who really don't like playing games where it is probable (or in some cases possible) to loose, people who don't like to read and only play very visual games, people who don't have enough familiarity with English to play games with a dependence on complex text (in the game or exterior wikis, etc.), significantly disabled gamers who are limited in their input and/or output processing in such a way that it is difficult to interact with more complex games, people who only play "popular" or "trendy" games due to social factors, people who prefer games with low or very low levels of violence and/or realism, and so on.
So we've taken a *very* small fraction of humanity, and shaved away all these other chunks. Even a massive classic like the Civilization series aims at a pretty small chunk. Anyone who plays DF, by virtue of all the above, is by any rational definition many standard deviations away from human average.
That said... the average DF player's age is highly likely to be *far* higher than you think. Older gamers are significantly more used to text-based interfaces, tile "graphics", turn-based games, and various other criteria. People who grew up on classic roguelikes (in the original sense... Rogue, Moria, Angband, Nethack, and so on) find the similar interface of DF comparatively easy to understand. Those with outside responsibilities (jobs, kids, volunteer commitments, and so on) are more likely to gravitate toward games that don't require specific times, don't require coordinating with other people, and can be paused, stopped and resumed at any point with no problems.
I"d guess that the two largest groups would be Gen X-ers (grew up with older computers, have a life these days) in the 35-50 year old range (and probably sliding toward the upper end of that); and current or recent college and graduate students (expanding horizons, tend to get obsessed, seemingly lots of free time) in the 18-25 year old range.
As for me? If you remember what "frog-knows" means as a version number without having to search it, you're in the right category.