What makes you so confident that they are using a Peltier? Here's their description of the operation of the device:
During adsorption, air is circulated around the MOF layer and water from air is adsorbed. Passive radiative cooling lowers the MOF layer temperature below the ambient by dissipating thermal radiation to the clear cold sky to increase the effective RH for adsorption. During water production, the OTTI aerogel is stacked on top of the MOF layer to suppress convective heat loss from the solar absorber. The desorbed vapour is condensed on a condenser and the heat of condensation is rejected to the ambient by a heat pipe heat sink.
And here's the more complete description of the condenser:
The condenser of the device was fabricated with a copper plate (4 cm by 4 cm and 0.6 cm thick) attached to a commercial air-cooled heat sink (NH-L9x65, Noctua) to efficiently dissipate the heat from condensation to the ambient.
Are you still sure it's condensing on a Peltier cooler? The paper never mentions "Peltier". If the "condenser" is actually an electrically driven Peltier, this would seem like a fraudulently bad description, justifying retraction of the paper. Is it possible that you are wrong?
Still, I agree that you might be right about the physical limitations of scaling. You seem knowledgeable about the field, and I'd be interested to hear your impression after you read the actual paper: https://www.nature.com/articles/s41467-018-03162-7.
(I am genuinely interested in hearing your opinion about what they are doing, but would strongly suggest less overconfidence and more humility when offering bombastic pronouncements on papers you haven't read.)