VG and PG are hydrophillic and absorb moisture, but only to a point. The info you linked to is talking about absolutely pure chemicals (lab type). The ones we know are already hydrated so they have no dehydrating effect. That's why both appear regularly in skin care stuff, moisturising shampoos etc - they are used to retain moisture (just as their use with tobacco).
I thought of one way that vaping would increase water loss, but it has nothing to do with VG / PG - when vaping we blow out air from the mouth whereas in normal breathing mostly through the nose (that longer path releases less water). But that isn't going to add up to much!
Yes, PG is hygroscopic, but it is also miscible with water. It doesn't matter if PG is in water, the effects can still occur. You are only talking about dilution at this point.
Unfortunately, it's a bit hard to find actual studies of composition of e-liquid, but here is one example of testing of Crown-7 liquid. Among all of the other components, it was found to contain at over 60% PG Wt-%, and over 8% water Wt-%. However, the vapor had over 2% PG Wt-%, and the water was over 66% Wt-%. Granted I don't have numbers for every liquid we vape, because frankly there are a severe lack of studies to provide the results. But based on the above, I don't see how that can be considered hydrated.
I found a couple more that didn't list water at all (though more likely they either were not testing for it, or didn't include it in the list for whatever reason), and one with water content less than 1% in the liquid (no composition of vapor).