I think the actual source for the article must have been the National Geographic's own article,
here, rather than the original AJHG paper.
From reading the paper and some of the references I can't see the support for a lot of the claims in the CNN article. Particularly I can't see anywhere in the paper where they discuss the estimated population size of 2000, wherever they reference that paper they don't do it in that context and I don't see how it can be described as noting that the study shows it. The National Geographic article on the other hand does briefly mention 'Previous studies have shown that while human populations had been quite small prior to the Late Stone Age, perhaps numbering fewer than 2,000 around 70,000 years ago...', although it doesn't give a reference.
So in fact the whole extinction thing seems to come from a totally different paper, so its a bit of a shame seeing that plastered up as the headline for this paper.
Were there any particular technical methods you were interested in? I have studied human genetics somewhat and I'd be happy to see if I can find some resources to clarify things but the paper does quite
a lot of different things so if there were specific things it might make things easier.
TTFN,
WK