That warfare and imperialism in the Mediterranean world may have been different, on average, than in other major centers of civilization seems possible.  I don't think you can say it dates back to the Romans, though, as the Assyrians seem to have set a strong precedent.

Then again, as has been mentioned elsewhere, the Qin Emperor was pretty damn nasty.

That Europe imperialized to a greater degree than other regional world Empires was entirely due to their luck of discovering the Americas first, and their ability to take advantage of the disease gradient.  Without that, the colonization of the Americas would have been a lot more like the colonization of Africa - which went absolutely nowhere until the the mid 1800's.  Without American gold and silver, Europe would have never been able to break the pre-existing trade networks of the Indian Ocean, and world history would have been so utterly and completely different that it's not worth discussing.

That Europe has culturally evangalized to a greater degree is debatable, given the immense spread of Islam.  It's too early to tell if the current fad for European culture and values is a passing fad, or a longer-term thing, but it's pretty clear that Islam is here to stay in Central, South, and SE Asia, and North Africa.