The structure can operate well enough using day/night variations. It would cool at night and collect dew in the morning as the air warms. No power requirement. It has to be very large to provide a significant amount of water.
But when I lived in Yemen, the 40°F temperature swings from day to night rarely produced dew clinging to any structure as there was next to no moisture in the air to collect. They may have done something to encourage the water molecule to cling to the material. Could be a similar concept to the mentos/diet coke formation of CO2 gas bubbles.