None of this matches the setup the paper describes, though of course you are right that bleeding heat into the Earth is a time-tested and known to function way to build such systems.
From the article:
> Before they understood what was happening, the researchers first thought that water was simply condensing onto the surface of the material due to an artifact of their experimental setup, such as a temperature gradient in the lab. To rule that out, they increased the thickness of the material to see if the amount of water collected on the surface would change.
There's a temperature gradient in their lab setup. i.e. one side of the material is cooler than the other side. This is where I extrapolated that you can increase the performance of the material by bleeding the heat into the Earth.