I'm bummed that you're getting downvoted for what's IMO a very natural question, especially given that "times" is unambiguous and that folding naturally implies a doubling. But this is English, it's deliberately designed to not make sense (see also the modern definition of "literally").

mumbles something else about 2^15

I think its getting downvoted because they suggested that the article's copyeditor should have caught it, despite the article being right. I doubt they would have been downvoted if they just asked, but suggesting that someone failed at their job despite them actually doing it correctly tends to get people a bit uppity.

Words are arbitrary, but there really isn't any dispute what -fold means as a suffix. See the dictionary entry for it https://www.merriam-webster.com/dictionary/-fold

Also as far as i know, this isn't just an english being weird thing, most germanic languages use "fold" the same way.

> folding naturally implies a doubling.

Why is that? I can imagine doing two folds on a sheet of paper and ending up with three layers of paper. Imo one fold adds one layer.