I think you need to take the whole phrase: "stood in the eye of history". That's what signals the eye=centre meaning. (Not that it would be terribly easy to stand in the eye of a hurricane, but it sure would be exciting once you got there.)
You might be right, c_b, but this could also mean that all of history was watching this election. That's how I read it. In other words, not only was their universal synchronic interest (the whole world), there was also, figuratively for the hopes and dreams of past generations, diachronic interest in the election.
I thought it was interesting that this phrase uses "eye" as in "center," like a hurricane, rather than as in the organ of vision:
"...The Guardian newspaper proclaimed: 'They did it. They really did it. So often crudely caricatured by others, the American people yesterday stood in the eye of history and made an emphatic choice for change for themselves and the world.'"