I've been playing on the 6th difficulty, and it's a good challenge. With Egypt, I kill everyone, but I haven't found another civ that I like all that much. My strategy is basically to get ahead with science tech, and build all the wonders that come from that. Building the Great Library early gives me a great head start on the other 7 Civs, so I can build every wonder that I want. This is a pretty common strategy, right?
What you're doing -- out-teching your opponents -- is a common strategy and a good idea. And the way you're going at, through certain wonders, is generally common in the mid- to late-game as those +Great Scientist wonders become available.
The part I don't endorse is doing that with Great Library. At the more advanced difficulty levels, going for Great Library is not common because it's usually not available to the player as the AI will get there by Turn 40 (at the latest) without fail. Even if it were available, it wouldn't be a sustainable strategy because in going for Great Library you'd be putting yourself behind in other crucial pre-Turn 50 requirements.
To be honest, G. Library is one of the least worthwhile wonders, especially if you're looking at just the early wonders. GL gets you at most ~200 free beakers. And that's it, your civ is back to where it was otherwise, all that infrastructure you delayed to rush GL now needs to be built up: archer/walls (if Immortal or Deity), settler, caravan, you name it. Those are early units you need, especially the settler. There's so many ways to get at that early science besides GL, but there's really only one way to get a solid pre-Turn 100 empire going: efficient production. And GL gets in the way of that.