Wonderful videos, and they reveal a lot. For instance, when the wings first unfold the tips remain bent up at an angle for a while, but then they straighten out and remain fairly stiff. It seems like that could be via a hydraulic mechanism (i.e., pumping fluid into hollow veins to straighten them out).
However, my main question is, how do they fold them up again? Sure, they could pump the fluid out again, but that would just make the wings foldable, it wouldn't do the actual folding, which would require some other mechanism. One possibility, which I don't take very seriously, especially after seeing the videos, is that the "hinges" are spring-loaded, and that they spring back into the folded position after the pressure in the veins is removed.
I wonder if a video of quality similar to these but that showed the folding process (from the outside, of course), would shed some light. For instance, if they showed some kind of rhythmic movement of the outer wings or of the thorax, that could suggest a friction-based mechanism that draws the under-wings inward incrementally.
BTW, I'm glad you posted the excerpt from the article, because the PDF didn't open for me.