The method from TFA uses direct evaporation and it produces solid salt instead of liquid brine.
The innovation is that this can work as a continuous process, at a high production rate.
The traditional method requires waiting a lot of time until all the water evaporates, after which there is a long and expensive interruption, when you have to gather the salt and clean everything, to be able to fill again the installation with sea water and start another cycle.
Because of the high cost and low output rate, the traditional method is typically used only for the production of salt, not for the production of potable water.
For potable water, the currently used methods are mentioned in the article, and they produce a lot of liquid brine instead of a small quantity of solid salt, and that brine is difficult to dispose off.
From the article and their paper it is not clear how they intend to scrape the salt deposits from the untreated part of their panels.
If you ever tried to clean seasalt from your car or boat for example, it's not a trivial process and is best done by washing it away, which is counterproductive in this case. Mechanical scraping would likely either damage the panel or not clean it enough besides requiring moving parts which is costly.
So it remains to be seen if this is useful at large scale.
Solar desalination looks pretty good in terms of efficiency. The problem is that the solar energy must now be collected at the shoreline. This means that a lot of coastal real estate gets turned into a desalination plant. Alternatively, you transport the water, but pumping seawater requires corrosion and fouling resistant materials throughout the system.
Just do direct evaporation like it's been done for thousands of years. If you don't like brine, leave it to dry out too.
If there is not enough sunlight, use direct nuclear heat.