There is a fundamental minimum amount of energy needed to desalinate: you can't take less energy to do it,than you could gain back (from osmotic pressure) if you allowed the desalinated water to expand a cylinder containing the residual brine. This is large. This paper is a thermal method, so it doesn't have an electricity input, but to justify their efficiency claim, they should really compare against what you could do by using the same surface area for solar panels, driving a conventional setup. My (limited) understanding is that conventional reverse osmosis is not far from the theoretical optimum, energy-wise, the main difficulties being operational (the membranes need declogging). And of course RO is more expensive than rain.

This paper is interesting, however, in directly producing crystalline salt, which is lower volume than brine and easier to dispose of, maybe even valuable.

If this can be applied to mine effluent, you could replace the maybe with most certainly. Sulfuric acid effluent lakes leech all sorts of valuable metals out of the ground.

Brine is very easy to dispose of: you just pump it back to where it came from. Solid crystalline salt, on the other hand, is a hassle.