If you read the study itself, it claims that it's still hard to say what the relative roles of ice age climate change cycles vs. human predation were on the extinction of large Paleocene mammals in North & South America (and Australia):
> "Despite decades of research on extinction causality, the relative importance of late-Quaternary climate changes and spreading human impacts have been difficult to disentangle because poor chronological resolution in the fossil record has precluded alignment of these rapidly occurring, tightly linked phenomena."
However, it seems pretty clear that wherever humans showed up into new habitats where humans and large animals didn't have a shared ecological-evolutionary history (i.e. not Africa or Eurasia) extinction rates among the megafauna shot way up:
https://ourworldindata.org/quaternary-megafauna-extinction
> "Africa was the least hard-hit, losing only 21% of its megafauna. Humans evolved in Africa, and hominins had already interacted with mammals for a long time. The same is also likely to be true across Eurasia, where 35% of megafauna were lost. But Australia, North America, and South America were particularly hard-hit; very soon after humans arrived, most large mammals were gone. Australia lost 88%; North America lost 83%; and South America, 72%."
Maybe large animal populations had shrank due to the spread of glaciers during the Last Glacial Maximum era (c. 25 kya) so they were more vulnerable, but the new factor (relative to the past 2.5 million years of ice age cycles) was the human predation.