"Share DNA" does not equal "prodigy of". In any event, he could have had one child and that line could have then been prolific.
Mathmatically, genetic mixing occurs faster and more broadly that you might imagine possible.
Do you mean “progeny” of?
To elaborate on the math (which I'm sure you know but weren't pedantic enough to post), in the 3340 years since Tut got wrapped up for his museum career, with one generation per 20 years, you would expect 167 generations. Assuming two survivors from each generation, and no intermarriage, that gives 2^167 offspring or far more than the 2^33 people in the world. Intermarriage of descendents cuts that number, obviously, but it's no surprise that someone who lived so long ago would have either a huge number of relatives today or none at all. I'd guess even Steve Martin is on the list.
I agree that if he impregnated of enough women so half of Europe is decended from him, Tut would have been a ‘prodigy’ indeed—but his descendants would have been his ‘progeny’.