Scientific results, the precision of their measurements.
I would not think leaks would be all that possible given the design. Essentially a membrane for water vapor to pass through, energetic water molecules. Surface tension plus the absorption of the salt should prevent liquid water from getting past the membrane.
The major sticking point is they are not talking 24/7 operation. They specifically give it a timeline, though they didn't provide the heat load itself, so don't be thinking desktop or laptop levels of power, probably a tiny heat source. So they rely on rest periods for the salt to reabsorb moisture.
Conceivably you could hook this up to a simple water supply, but at that point there are surely better options. (That or you need two chips/coolers, one to run and produce the moist air, and the other to absorb it while idle)
Or my silly solution, drippings off of a Peltier device.