and what do they do with the super heated concentrated salt solution left after the superheated water is evaporated?

It is good that there is some effort to make systems not dependent upon high cost and maintenance, reverse osmosis filtration.

Does this require oil for its production?

@analogue girl the desolenator uses the heat from the brine through heat exchange. The output brine is low concentration and can be recycled through the system. Brine waste is a challenge, we are looking at halophyte crops amongst other solutions such as easier running back into the sea in a coastal context @Freyr fossil fuels are used in industry production yes, however there is an energy ROI. In future we hope that manufacturing will be powered by clean tech but it will take time

Why use all that fancy expensive technology, what's wrong with a simple solar collector boiling the water and condensing the steam?

Using the electric components seams awfully expensive. I would either uses a conventional solar still or use a foil reflector and a vacuum inducing condenser. And if I was feeling really ambitious use a Sterling engine to generate a little mechanical energy while pulling the waste heat out of the condenser and brine.
@ analogue girl
Pour it into an open basin and let it continue to evaporate the water out and then pile the sold matter (Mostly salt) into piles.
Adding a little salt to some clays makes the dried mud much stronger.

Next stop, Mars?

Analogue girl brought up a good point about the waste salt but most importantly is that they stated they run the water down across the panels. Brine water running down will eventually clog the system. It can't run constantly since it needs sunlight. So at night the system is stagnant. The brine unless flushed will build up residue. The system requires constant flushing to sustain brine operations. Corrosion will be a strong concern.

I could live on 4 gals a day easily

It is amazing to hear that this machine is able to produce so much clean water! It would be really great to look into this option to see if I could get one for my family. Then if we ever were to have problems with our electricity or plumbing systems, we could still have clean water for drinking and cooking. Thanks for sharing this!