Am I missing something? The water vapor needs to be collected via condensation, but it doesn't seem that these objects contain anything for that - or even to be designed to make that possible.
It seems they are only solving for two problems of solar desalination: to efficiently (1) transfer heat to a small amount of water, so it can evaporate, and (2) remove the brine from the device.
Once the water evaporates, you can probably just condense it via standard methods that are both passive, and extremely efficient. So they don't bother doing it. Basically, this thing will be surrounded by some apparatus that collects the vapor.
These are tiny little things, less than 4cm in diameter and floating on seawater. They rely on the sun shining on them to vaporize the water, and in fact the linked paper says that the convection cover is needed when outdoors in the wind.
So... it implies that you can't have anything blocking the sun from fully shining on it, because it already has enough problems gathering enough heat when the wind blows, right?
Where does this condenser go? Obviously, I don't know anything about engineering in this domain ;)
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.
The hard part of distillation desalination is the evaporation. Condensation is pretty easy, just run the vapor laden air through a long metal or glass tube and it will just happen on any nucleation sites if the condenser is cool enough. You can even use some additional salt water to cool the condenser.
Once the water evaporates, you can probably just condense it via standard methods that are both passive, and extremely efficient. So they don't bother doing it. Basically, this thing will be surrounded by some apparatus that collects the vapor.