I don’t think I fit either side of this dichotomy (though if forced to pick would choose extrinsically), as I love a good story but am very much about the journey and not just the destination.
If I had to guess, the limits of development scope and the resulting limits on worlds being believably reactive means a lot of people are going to see themselves as extrinsically motivated, with the big exception being people that just love building things in sandboxes. Intrinsic motivators would be much easier to come across if more avenues of interaction felt fleshed out but for some rare exceptions.