Most fabric layers are more air than fiber; so, it is the water in the spaces between the fibers and layers which are the primary determinate of saturated weight gain and inversely, the drying time. If two fabrics are the same weave / thickness but, made with different thread material, then the material with the lower regain will dry only slightly faster.
I think the original text under "mm Thick", your description, and the above alternate description all attempt to convey the same meaning. If you have a suggestion for making "mm Thick" text much clearer without being significantly more verbose, I will change it.
The primary research paper in this area said, "The main fabric property which does determine the amount of water a fabric freely picks up is thickness. Further, the time that it takes a fabric to dry is directly related to the amount of water which is in the fabric initially, the more water it holds initially, the longer it takes to dry. Finally, water evaporates more rapidly from a fabric than from a water drop of equivalent volume. This is because a fabric has a greater surface area from which the water can evaporate."