So where does the water go? If the protein eventually becomes full of water, then it's power storage, not generation.
HOWEVER I've been studying biogenesis within c3/c4 plants and there are some fascinating structures inside natural systems. I'm amazed at how little we actually know.
The hot new science trend of 'biomimcry' uses a lot of inspiration from those natural systems - many of the inventions use a combination of hydrophilic and hydrophobic membranes that accept, transform, then excrete the byproducts (almost like a pump).
The membranes themselves are often exotically doped chemicals and/or graphene carbon-nanotube structures which exhibit all sorts of weird nano-scale behaviors that replicate things we take for granted in nature (i.e. did you ever wonder how water gets to the top of a giant redwood without a pump?)
A gradient can be maintained between different layers of a membrane (the recent example of generating current from rainwater used a highly exotic modified form of a FET/BJT as the water oxidized across the metals to collect and transfer a charge as the water moved across it).
If the end by-product is dissipated with diffusion (or in this case a water condensate and gravity) it is possible to create structures that use that surface tension of water to move against gravity pulling the moisture through it.
Additionally are algae's (proteins?) which can perform photosynthesis with both sunlight and moonlight, and others that work in complete darkness and even generate their own light (bio-luminescence) or heat.
There is a lot of 'free potential' within entropy so pulling a few mV out of the chaos isn't' inconceivable.
You usually have to expend energy to get water out of the air, no?
And any process which provides energy-free dehumification would also have the secondary (or primary) benefit of providing energy-free freshwater.
I'd imagine they've thought of both the above applications, and their protein nanowires aren't suitable.
I'm sure the researchers have thought of this, but it wasn't in the abstract.
Still a really cool advancement, but not some magical de-humidification technology.