unfortunately the terminology here is very unclear, but i think you're right; the megafauna dying in america was the https://en.wikipedia.org/wiki/Late_Pleistocene_extinctions and happened before the https://en.wikipedia.org/wiki/Younger_Dryas, which is the '1200-year ice age' whose name the nyt didn't think was important enough to mention

https://en.wikipedia.org/wiki/Younger_Dryas_impact_hypothesi... discusses the comet impact hypothesis, which it describes as 'controversial and not widely accepted by relevant experts'

also note from https://en.wikipedia.org/wiki/Younger_Dryas that the younger dryas didn't happen in south america, which is where the largest extinction of american megafauna happened; instead south america had the milder and earlier https://en.wikipedia.org/wiki/Antarctic_Cold_Reversal

however, it seems obvious that a widespread glaciation would have caused some extinctions, and there was a long tail of megafauna extinctions that extended long after the younger dryas. glyptodonts like https://en.wikipedia.org/wiki/Doedicurus apparently didn't become extinct until only 8000 years ago, and the wrangel island mammoths didn't become extinct until only 4000 years ago