I don't deny that humans were responsible for eliminating some species. The moa's extinction happened in historical times and humans were the cause. I don't dispute that humans hunted some of the larger animals but I have a real problem imagining that small bands of hunters could wipe out the entire range of megafauna. The matter remains a totally open question in my mind.
Many animals not used to humans show no fear of them, and thus were easy to eliminate before they could adapt.
As we have seen from the spread of invasive species (in Australia and elsewhere) a new species tends to throw things out of whack, and they make a huge impact within a short time.
Of course it isn't the sole explanation, and the data is far from conclusive. But the data seems to show that when humans showed up, a lot of mega-fauna soon disappeared.
And it doesn't take “bloodthirsty” or “short-sighted”; it just takes an easily exploited resource and hungry people.