It also looks solar powered-only, so its efficiency is not better when the dew point is closer (night/morning).
Linking a small solar cell (I would say ~1W from the shown surface) to a Peltier element (known power hog, a really small one takes at least 4W) is not a solution for efficiency.
Wolfram alpha says it takes ~1.3kj to change the temperature of 1m^3 of air by 1 degree C.
Obviously this will vary enormously with temperature and humidity, but it gives us a number to work with.
Wikipedia, and a post by 'someone' tells us there is ~30cc of water per cubic meter of air at 100% humidity and 30c. (This could be a reasonable set of envoronmental conditions in Washington DC for example).
So we can extract ~3g, or 3cc of water from saturated air, with the use of ~2.6kj (assuming 100% efficiency, which is unlikely)
Some of the highest power density batteries I've handled are 5 cell, 5500mAh li-poly batteries for model aircraft use, with a total energy capacity of around 180kj,
Linking a small solar cell (I would say ~1W from the shown surface) to a Peltier element (known power hog, a really small one takes at least 4W) is not a solution for efficiency.