The article doesn’t address the question of how the cup truly works. It relies on capillary action but, based on the article, I’m not sure how.
The first analysis of the effect I know of is a paper by Concus and Finn (1969) [2], who realized that fluid can be carried arbitrarily high in a triangular groove, even against gravity, and proposed that trees may use this mechanism to carry water to their highest reaches. (The catch is that the fluid front becomes thinner and thinner as it gets higher. And it starts breaking down when it gets so thin that the continuum limit no longer applies).
If you like math, I'd highly recommend checking out Mark Weislogel's research [3] which deals with the dynamics of viscous flow in triangular grooves.
Shameless plug: chapter 4 of my Ph.D. thesis [4] gives an introduction to the subject.
[1] http://www.pmdtechnology.com/PMD%20Physics.html
[2] https://doi.org/10.1073/pnas.63.2.292
[3] https://scholar.google.com/citations?user=rNOJ49QAAAAJ
[4] https://theses.hal.science/view/index/identifiant/tel-040155...
But, for exactly the same reasons, this thing is probably a pain to clean. Sharp corners and cleaning don't mix. That narrow seam will likely become caked in the dried residue of a hundred previous drinks. Even in an earth dishwasher, soap scum would be difficult to rinse out. I suspect these are not used many times.
On the other hand, without gravity there is convection, which means those corners probably don't dry out as quickly. If I'm right about that then rinsing left-over residue out with plain water is easier if you don't wait too long.
I dunno, given the size I imagine a regular toothbrush could dislodge anything dried, and small sponge-on-a-stick could get it acceptably dry.
It's also worth asking what it might replace: On the ISS do they clean any drink-pouches, or are they all treated as disposable? I imagine that they become trash, since the next drink (or dehydrated drink-to-be) was probably already shipped in its own flattened pouch.
I think it works because the narrowing channel has increasing surface area to volume ratio, as you proceed toward the spout, so the capillary forces pull along a gradient toward the spout, gently tugging the liquid toward it.
The bowl of the cup is lightly pinched around the brim to provide a kind of barrier to prevent the globule of zero-g liquid from just floatin' away! Hahaha :)