Interesting read, and above quote shouldn’t distract from it, but I thought that theory was abandoned, or at least certainly not considered so likely that it would be presumed by default anymore.
https://www.smithsonianmag.com/science-nature/what-happened-...
and yet you've linked to an article that goes into detail about work that
may be close to a deathblow for the hypothesis.
First proposed in 1966 by paleontologist Paul Martin, this “overkill hypothesis” stated that the arrival of modern humans in each new part of the world brought with it the extinction of all those huge animals, whether through hunting them or outcompeting them.
The Smithsonian Magazine here is being wishy washy and doing the "good points on both sides" thing .. it at least admits that the world has moved on from accepting Martins 1966 hypothesis at face value and that new work is continuing to reveal new insights.
The second does not imply the first, correlation is not causation.
> what other theories are beating that out?
See: almost any scholarly discussion on megafauna disappearences in (say) Australasia or elsewhee of the past few decades.
TL;DR: no theories are beating it out human overkill. Megafauna need to show a mass extinction sans humans and that evidence is lacking. These animals survived a couple dozen ice ages but the final one ends their existence when humans arrived. We would want more hunting and butchering evidence and Africa kept much of its megafauna. So there are unanswered questions but overkill is still largely yhe leading theory
Your article is a PopSci "both sides" summary that reinforces the notion of correlation and not causation.