I’ve not heard the term used that way—I’ve always understood it to indicate a multiple. But now that you’ve said it, the idea of -fold as “folding something in half” is interesting to think about!
I don't know if the engineering field has the same conventions, but in biology we use "fold" as it was used in the paper.
When comparing the signal of two things, the fold change is how many times one is bigger than the other (basically A/B). If A is 15-fold higher than B then it's 15x B.
What you described is the Log2 Fold Change (log2(A/B)), meaning that if A has a log2FC of 15 over B, its signal is 2^15 times higher, hence ≈32,000x.
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").
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.
I feel like someone should have caught that before publication.