I don't think there's any set formula for deciding a good game - you either like it or you don't.

For example, I'm a huge RPG fan, but storyline is hardly necessary for a good game. Counter-Strike has absolutely no story whatsoever, yet it's one of my favorite PC games.

The same holds true for gameplay. The battle system in FFIV is actually pretty unoriginal and alot of the time boring, yet it had a great jRPG story for the SNES era.

For a game to be really great it has to have all of the 4 poll choices, including graphics. While graphics alone is never a good way to rate a game other than on aesthetics, it reinforces all other aspects, to drive home story and gameplay in ways that games with lesser graphical focus simply can't. Music I feel works in the same way.