The prototype is 4 cm in diameter; the actual device would be much larger. This one evaporates about 1.3 Liters/m^2/h at peak conditions. In a day, in practice, I doubt it would produce more than 1.3 * 50% extra losses * 6 hours = 4 liters.
For a family of 4, you need maybe 3 liters * 4 = 12 liters in a day. So you need a 3 m^2 device to satisfy them. Or something on that order.
Finally, this thing will probably be encased in a glass chamber, which will collect the water vapor and then condense them in some container. So that is a whole other additional cost. So, yes some sunlight will be blocked or reflected by this additional structure.
If you do a quick image search of "solar desalinator" you will see plenty of examples of how this condensation works.