Descent from Genghis Khan revisited

My niece Sophie reckons I shouldn’t be so quick to give up on the Genghis Khan ancestry (see more here). She vaguely remembered something about him breeding like a bunny from Anthro. 101 genetic trends, but also pointed me to a New Scientist article “that suggested that Mongol emperor Genghis Khan has 16 million descendants after conquering most of Asia in the 13th century”.