hi! Similar questions come up in this sub quite often, i.e. "Is Genghis Khan/Charlemagne/William the Conqueror/whomever really the ancestor of x% of all Asians/Europeans/British/whomever?". The question is really more applicable to /r/AskScience (under the categories genetics and mathematics), but the TL;DR is yes: broadly speaking, everyone who lived several hundred years ago - and not just kings, I mean even goat-herders - who produced at least grandchildren is the ancestor of a great many people living today.
Here are the most recent posts on this:
and see this one, which has a longer explanation of the math involved, plus links to several other posts, including an excellent AMA in /r/AskScience with a pair of geneticists
A couple of caveats when reading these threads, since comments are not always clear about what they are referring to:
"Descendants" are Genghis Khan's children's children's children's ... children. As a hypothetical example, imagine that after 2 generations he has 4 children (2 sons and 2 daughters), each of whom have 4 children (2 sons and 2 daughters): that's 4 + (4*4) = 20 descendants.
"Male-line descendants" are Genghis Khan's sons' sons' sons' ... sons only. Using the above example, after 2 generations he has 2 + (2*2) = 6 male-line descendants (that is, his two sons and their sons; his daughters, his sons' daughters, and his daughters' children are excluded). This is the group that Y-chromosome DNA evidence refers to (see next point).
Y-chromosome DNA evidence does not prove descent from him personally, but from people with genetic markers which he (may have?) shared
You can't actually frame the problem like that. You can't say for certain either how frequently Genghis Khan impregnated women or what having Genghis Khan as the father did to the longevity of his offspring. (Did more mothers than average smother them at birth? Did his offspring tend to have higher social status and themselves produce more children?)