Most of these questions seem to cut towards the same matter.
This is probably my favorite (and certainly most linked) Extra Credits episode, on Aesthetics of Play.
Dwarf Fortress can satisfy four, possibly five different aesthetics directly, and in the meta-game, another. This is far more than most, and that's because it's such an expansive game that someone playing Adventure Mode is doing something leagues different than a megaproject builder which is leagues away from someone modding in nightwing siegers or challenging the HFS with nothing but straight dwarf power for a bigger, tougher fight.
Challenge - The most "classic" aesthetic, many players just feel that being "hard" is the only thing a game
should be. These are players that declare they need to mod new, bigger siege creatures in, no crossbows, no traps, melee only, Final Destination.
Discovery - Fortress as experiment. "Losing is Fun" is the tagline of the game, but I tend to see it in different terms than most. Losing is Fun might mean your fortress crumbles to a challenge player, but to me, it means Learning is Fun. The game is only fun if you learned something from it. If something bad happens, and you couldn't figure out why, it's just random and arbitrary and unfair. If something bad happens, and you can discover why, and how to pre-empt it, it's a learning experience, and Learning is Fun. Exploration in Dwarf Fortress isn't exploration of a map, it's exploration of the vast world of emergent interactions within the vast jungle of game mechanics. Discovery players are the most likely to build whole forts exclusively to !!SCIENCE!!, and won't be ashamed to start modding dwarves in ways that make the game "easier" to test things out.
Expression - Fortress as Lego set. Expression is the joy of creativity and individuality. Expression players are fanatical about the appearance of their fortress. They are the sort that would obsidian-cast their whole dining room just to force it all to be one color. You can see these players from a mile away on the forums because they're using Overseer and Stonesense and showing off the fact that they built a 50-z-tall statue of a dwarf cleaving an elf in half while the elf bleeds a waterfall of magma blood. Players who are exclusively focused on expression will probably turn sieges or other "challenge" features off to help them focus more exclusively upon their goals.
Narrative - DF as story-generator. DF as The Sims with more blood and battleaxes. This is probably what Toady leans towards more than anything, himself. There's a Hall of Legends for a reason, and for a good while, the single biggest reason anyone would give for why they started playing DF was "Boatmurdered". Narrative players are distinguished by the fact that they name their dwarves with "proper" names (mythic names, names based upon their personality, named after their friends, just named proper names in general,) as opposed to naming based upon function, and many prefer smaller forts, since giant forts where you simply have "Hauler #32" is anathema to narrative. (Alternately, they may try to go without nicknames at all, and learn each and every Ast and Urist.) Narrative players may be the most unpredictable about their risk aversion, as they may grow extremely conservative to try to protect their precious dwarves one moment, and then decide it's time to open up the caverns and take on an FB because it's been too safe and boring for too long the next.
Fantasy - This one is more sketchy, although players who are primarily interested in Adventure Mode may well fit into this aesthetic. Fantasy is the enjoyment of "being someone else". The line between Narrative and Fantasy is somewhat subtle, but it's basically whether it's a story you are
observing or telling, versus one where you are
acting it out. Fantasy is more likely in Adventurer Mode than Fortress Mode, because you more clearly are one specific character. (At least, outside of hermit challenges...) That said, Fantasy proper takes actual role-playing, rather than "I'm going to see if my adventurer can kill that thing!" Fantasy players are probably the ones most likely to be modding in the random not-dwarf things like My Little Pony, though, because they're more interested in who they're supposed to be than what they're actually doing. Fantasy players are more concerned about the ethics of their characters or how the game world would see their characters or how happy their dwarves are.
Fellowship - The meta-game. Dwarf Fortress as conversation starter. Some people don't play the game so much as they enjoy the forums, itself. DF wouldn't likely be capable of sustaining itself without Bay12, and the fact that people want to keep coming back and sharing what they do in this game.
Nobody is just one of these exclusively, especially since a major part of DF's draw is that it plays upon such a wide variety of aesthetics, and a person who simply wants
challenge and
challenge alone is probably playing competitive RTS games, instead. Nevertheless, there are obvious preferences when someone dismisses another person's giant castle megaproject because they used some sort of mod or hack to vaporize excess stone or turned off invasions as "cheating" when they, themselves are using mods to add tougher enemies, only.
Still, if you want to categorize players, you might want to do so by asking a series of questions that let you rate each player as a percentage of each of those aesthetics. Rather than having some giant lists with a "pick one" for "favorite challenge", I'd suggest you have one of those 5-point "strongly agree, somewhat agree, neither agree nor disagree, somewhat disagree, strongly disagree" polls with all those challenges being asked as individual questions of how interesting such a challenge is to a player. (That or ask for a ranking system.)
For questions, I'd ask about how they mod the game, with that "strongly agree, somewhat agree, neither agree nor disagree, somewhat disagree, strongly disagree" spectrum.
1. I prefer straight vanilla.
2. I enjoy more powerful enemy mods.
3. I enjoy mods that make workshops more complex and detailed.
4. I enjoy mods that make the game simpler.
5. I enjoy mods that make more powerful tools or metals to make weapons from.
6. I enjoy graphic mods that are representative pictures.
7. I enjoy tilesets that are abstract but "cleaner" than standard curses.
8. I enjoy Stonesense to the point that I build my fortresses based upon how it looks in Stonesense, rather than in vanilla.
9. I enjoy 3d visualizers, and design fortresses to make them look cool in 3d.
10. I enjoy making complex 3d structures, even though I do not use any 3rd party tool to even see the resulting project. (It's all in my head.)
11. I enjoy making complex mechanical constructs like minecart-based clocks just because I can.
12. I enjoy things like Perfect World that let me have specific world types.
13. I enjoy Legends Mode or a Legends Mode utility like Legends Viewer frequently to understand my worlds before I embark, and enjoy reading about legendary historic features.
14. I enjoy mods that are "conversions" that let you play different sorts of creatures, or characters from some other franchise, such as Touhou or MLP mods.
15. I enjoy nicknaming each of my dwarves based upon making a more enjoyable story, rather than using it to designate their job function.
16. I cannot play the game without using DFHack plugins like Dwarf Therapist.
17. I take pride in the fact I refuse to play the game using any sort of "exploit", and consider more things "exploits" than most people.
18. I don't really play that much, I just haunt the forums.
(EDIT: Sorry Acrvasti, I revised it a little
)