I think the problem is, you might be looking for a “big pattern” that explains them all, while each separate extinction probably has its own unique causes. Humans cause some extinctions, other predators cause some, changes in habitat, climate, or availability of food sources cause others, etc.
I'm not really looking for a "master key" exactly, but in this particular case, I don't understand why a comet could wipe out camels and horses, but spare the buffalo.
I could see how hunting by humans might put enough extra pressure on a particular species - one that is already on the brink - to wipe them out; but the Pleistocene extinctions wiped out hundreds of species. I don't think humans hunted the short-faced skunk to extinction, for example.