Jiro's fallacy is not in saying that the world is or has been just in this respect, but rather in implicitly saying it must be. I don't think it's a coincidence that liberal/secular/enlightenment nations are the most powerful today, but that fact doesn't negate the point of the barbarian hypothetical.

I seriously doubt the viability of your Genghis Khan plan for modern fundamentalist Islam, seeing as that same M.O. was tried recently except starting with one of the world's top industrial and scientific powers. But that's a fact about our world, and the point of the barbarian example is more universal than that.