It's not like the other Empires around the world were Gandhian paradises of peaceful coexistence. They were waging war on each other, looting, and going on slavery raids just like Europeans. Go and look at Aztect ruins in Mesoamerica sometimes and marvel the the monuments where the prists were sacrificing humans.
Yet, despite the experience with war and violence, they (almost) never managed to beat Europeans, and certainly never colonised Europe (after the Muslims were thrown out of Europe ... Well ... depending whom you ask, the (descendants of the) Ottoman Empire are still colonising parts of Europe today ... Just ponder why Constantinople is no longer called Constantinople).
Why? What did Europe have they didn't?