Pillars? What Pillars?I've been thinking a lot about what really factors into a game, and how these things interact and all that. And in the end, it comes down to three things. Narrative, Aesthetics and Gameplay
The BasicsThere's some basic rules for this three pillar system. The most important one is that none of these elements should be badly executed. They should be mediocre at best, because no matter how good one of them is, if another one is bad enough, that won't save the final product. Also, these three elements are not absolute. Depending on the kind of game, their relevance varies. The quality of each pillar is always going to be determined relatively to its importance.
GameplayYes, I know, I put that last in the list, but really, it's kind of important in a game. Gameplay is the interactive part of the game. While it's usually quite important, mediocre gameplay can work if the narrative is good enough. On the other hand, you might just accept a flimsy plot if the gameplay is good enough.
NarrativeNarrative consists of the plot, the characters and the world the game is set in. The relevance of the narrative can vary a lot. Gameplay-related games often just have an excuse plot, because you're supposed to play the game for the gameplay. This doesn't make the narrative bad, since it's supposed to be judged relative to its importance for the game. A good story in a gameplay-driven game is essentially a bonus point that, ideally, makes the game even more fun and enjoyable. A good story in a narrative-driven game, on the other hand, is a must.
AestheticsAesthetics is what most people mean when they say graphics. Aesthetics are so misunderstood, Extra Credits made a video. In a nutshell: Aesthetics are not about the objective quality (amount of pixels, polygons and shading filters), but about how everything blends together and how well the end result looks and feels. Also, there's one difference to the other pillars here: Aesthetics cannot carry a game. A game is based on the interactive experience and/or the story it wants to tell. Aesthetics are a bonus point, and bad aesthetics sure can drag it down, as well as lift it up, but there needs to be more to a game than just that.
The ExtremesOf course, there's always people who focus on just one element and completely leave the others in the dust.
Gameplay - I swear, it's fun: Actually, I think it's really hard to mess up a game that only has gameplay. But if you really drop the other elements, you might just end up with something too unappealing to play, even if it would end up being a fun experience. But with these looks and that story, no one's going to touch it with a ten foot pole.
Narrative - go write a book: There can be such a thing as too much plot. This kind of game comes from someone who desperately wants to tell a story, but doesn't really get game design. This is a game you'd rather watch as a Let's Play than play yourself because it gets tedious.
Aesthetics - the spectacle: I would have liked to compare this kind of extreme to a movie, but then again, most movies have plot, too. So it's mostly like a 90s action flick that believes itself to be serious character drama. And for a movie, plotless BS can work. But a game has to be more than that.