I'm not sure I fit on that gamer/sandboxer scale at all.
While I like challenge, and I want to win, neither of those is my absolute primary goal. (I only play SP). On the other hand, I don't really have a strong need to roleplay or stick to a theme.
Probably Wauthan's 4th kids is most similar to mine, though perhaps I'd be a 5th kid: He avoids the others as long as possible, building up a massive elaborate castle with every possible weapon and defense, up to and including strategic nukes. Only when provoked or there are no new "toys" left to research/build does he launch his attack and utterly decimate the other kids castles.
So my ultimate game fun is to expand and tech up to be able to access the coolest spells/items/summons/etc, and then unleash these against my opponents.
Usually, it's possible to win the game well before those top techs become available, but I don't push to win, so that I can get to play with all the cool toys. That's also why I never go for dpilomatic victories or vitory-point victories in games that allow those types of options. Winning with iron dragons are so much more fun than with trolls...
So I guess I'm one part sandboxer, one part gamer, and one part munchkin. Or maybe I'm all munchkin/min-maxer, depending on how you look at it.
