Can anyone understand/explain the science here?
I've only spent less than 5 minutes reading about this, but the gist seems to be that the new materials are particularly effective dehumidifiers because they can be made with a very high porosity/surface area.
A dehumidifier works by pulling air through a cooled material. Water in the air then condenses onto the surface of the material, and can then be collected as a liquid. If you have a material with a higher surface area for a given volume (think of a sponge - lots of internal surface area compared to a solid block of the same size), then you will be able to collect more water, more quickly.
I don't know what it is about the new chemistry that allows the particularly high surface area materials.