My recollection was that they killed everyone, including children, who didn’t have another good use—in other words many of the females.
I watched about three minutes of a History Channel biography the other night and they made the point (as did Weatherford) that the Mongol genes are evident virtually everywhere in the world now because of the, ah, fecundity of Genghis and his crew.
Everything that I have ever read about Genghis Khan is that he let children under the age of 15 live. He also let the women live for the, ah, fecundity of Genghis and his crew. :-)
But you are correct about the genes being spread all over the world.