Well, from personal experience I can honestly say... none of the above.
Story? Did Shadow of the Colossus have a great story... or even a story at all? I never cared for the story in Halo CE, but I had an absolute blast playing coop and multiplayer. So Multiplayer? Nope, the majority of games I play have no multiplayer whatsoever. Gameplay then? HA! I fucking loved Vampire the Masquerade: Bloodlines and the gameplay was atrocious, and Psychonauts was pretty iffy as well but I sure loved it to death. Deus Ex AI was laughable, and the gameplay felt clunky. Mass Effect AI was no better, and nobody will remember it for its stellar gameplay. Graphics? Don't make me laugh. Genre... Sims, Painkiller, Mario Kart, Goldeneye, Starfox 64, Banjo kazooie, Thief, Zelda, Amnesia, FFVII, Mass Effect 2, Katamari Damacy, System Shock 2, Fallout 3, Neverwinter Nights, Wii Sports, etc... not much these games share in common, but I sure liked them all for various reasons.
I think the most important part of a game is that it is an enjoyable experience for the player, and at least in my case, there seems to be many ways for a developer to achieve just that.