I'm fairly certain they've created some form of a Brownian Ratchet: https://en.wikipedia.org/wiki/Brownian_ratchet
People love to claim there's no external energy source, but then when you look closely, you'll find a hot-cold differential, and then you need external energy to maintain that differential. I'd put a large sum of money that either the material is colder than the ambient environment or the incoming moisture is warmer than the ambient environment. It might even be a differential within their material, and the lab lights are warming one side! There's a lot of passive devices that rely on the hot-cold cycle of day and night, that still counts as energy input from the sun.
The article even mentions they tried to rule out a thermal gradient by increasing the thickness of the material, I'm not sure I understand why that would rule it out... the gradient would still exist.
I hate this, because if they aren't intentionally supplying energy, it's probably really efficient (assuming they aren't taking samples out of the freezer or something) so it's still a big deal and important but apparently we have to claim something is a perpetual motion machine to get attention among the public.