Well depends on what you mean by graphics if it just means mindless pushing more realistic graphics then no graphics of that short isn't that important and it can be said that games like this don't age well.
Games are a complex piece of multi-media, we you can have the best story in the world and if there is something mechanical wrong it can ruin the entire experience. (FPS stutter, unresponsive controls, bad sound choices).
But it can also be said it does depend on the genre if story even factors in on the game, you can ruin a game by forcing story elements into a genre that do not need one.
Looking at a game you can divide it into these pieces which I order in how important they are or in other words I order them in if some thing breaks does it have an affect on the lower ones if not the items goes down in importance. Also the items in each piece are about as import as the others in that level. So I consider a game with strong story elements in that the story has just as much importance as the art direction.
Here they are:
Background Mechanics: FPS, Control, Sound Mechanic (think the low health beeping and if sound works)
Game Mechanics: How the game interacts with the person, UI elements
Art Direction: Story, Sound Direction, Art Style
So If something is wrong in the back ground it affects how the game plays. If the UI is cluttered and the play mechanics are little wonky if things work smoothly and consitantly the game is still playable.
If there is something "wrong" with the art it doesn't have an impact on how the game plays. And usually down the road the games that were panned because of the art are all of a sudden great games or have a big cult following. You can think of Wind Waker. The outrage because of the graphics was something to experience.
So there is my two cents.
