To begin with, read Gygax's introduction to the 1st edition DMG. In it, he expressly states that his goals in the game are gamist in nature.
Unfortunately for me, Gygax didn't seem to understand that for me 'fun' contained more narrativist and simulationist aspects than D&D had at the time. For me, the fun was not in the gamist aspect of Role Playing - because if that was my primary goal I'd play Chess, Blood Bowl, or whatever expressly competitive game instead of a cooperative game. Moreover, even at an early age I became more interested in being a DM than a player. There are alot of things that attract people to DMing, but more me it's expressly narrativist (I've a story I want to tell) and simulationist (I like tinkering with the rules to make them more realistic, simulating complex societies, and otherwise making the game seem more real) goals.
I'd say that I was probably 45% Simulationist, 35% Narrativist, and 20% Gamist.
I am capable of - depending on the situation - going into fully Gamist mode and treating D&D in a competitive ('Let's see if I can beat the DM') or semi-competitive fashion ('Let's see what sort of devious challenges I can throw at the PC's'). I just long to do more than that.