Solar-powered desalination system requires no extra batteries

Unlke some comments are implying, this is not a solar distiller with "additional steps". It still uses far less energy than distillation as it doesn't involve phase changes.

It uses Electrodialysis, which is a mass separation process in which electrically charged membranes and an electrical potential difference are used to separate ionic species from an aqueous solution and other uncharged components.

Can't a lot of the phase change energy in distillation be recovered by using incoming water to cool/condense the distilled water vapor?

It would improve it a bit, but not enought to compete in terms of energy usage with dialysis or reverse-osmosis.

Reverse-osmosis is absurdly efficient compared to distillation: a single 1X1 meter square solar panel can potentially generate 200 liters of fresh water per day.