In a basic, high school English sense, a story has:
* a goal
* a conflict that represents the impediment to that goal.
* the resolution of that conflict.
In these loose confines, you can describe the way folks play games as stories. In D&D the goal is to level up. The conflict is that characters risk death or resource loss in attempts to level up. Resolution is episodic: campaign arc by campaign arc.
Where I differ from Mike is in the above: Note that my description above does *not* need to have anything to do with the game world or narrative flash. Really, a "core story," is what's invented after the fact from metagame concerns.
So "dungeons" and "loot" are really narrative skins for a way to power up and fight for said powerups. A series of wilderness treks does basically the same thing.
Lets look at Vampire:
In Vampire the goal is to remain socially viable by becoming more powerful without losing excess Humanity. The conflict pits character against stimuli that threatens their ability to become more powerful or retain Humanity. Resolution is, again, episodic.
It doesn't matter whether a Vampire game involves fighting elders or an in-depth examination of the consequences of feeding. They hit the same triggers.
However, outside of the gears that encourage a certain structure that flash *is* important to actually enjoy the same. To games of D&D and Vampire can have radically different moods, but cleave to the rules' suggested story. When something conflicts with the structure that the rules encourage, then things don't work so well.
As far as Eberron goes, the problem is that much of the doesn't really stick to the gears. There's no system for patronage, for example. It's designed to encompass the core D&D game, but the exotic elements aren't backed by much.