I don't think we can rule out it being mostly a cultural thing, given that sprinters all come from a specific location in West Africa where a very large pool of people receive world class training for such an event. 

Black people in Africa are also more genetically diverse than the differences between any two ethnic groups outside of Africa, so even if it is a genetic thing it probably isn't a "black" genetic thing. 

I suppose height might give a minor advantage in this case, and certain areas in Africa do have tall people, but that also implies say Dutch people should be good sprinters as well, or any number of other areas in and out of Africa that also gives more tall people.

 Outside of that, it doesn't actually make much sense that anyone would be particularly genetically adapted to sprinting. I mean endurance running was likely at one point important to human survival, but that's not really the case anymore even in Africa. What makes a good endurance runner isn't even the same thing as what makes a good sprinter....