Ancient humans causing extinctions and environmental change is at odds with the image of "indigenous societies are perfect environmental stewards", which has been popularized for various reasons.
Additionally, during the same time period megafauna in Africa have (well, until recently) continued to thrive despite the presence of humans and earlier hominids for millions of years.
The difference is that humans were not native to the Americas, and arrived rather suddenly some tens of thousands of years ago. Meanwhile animals in Africa (and Asia and Europe which were populated much earlier than the Americas) spent much more time co-evolving with humans as predators.
Why? They survived greater climatic change/habitat loss before.
Not unlike how our current wave of sustainability is a result of ruining our environment.