The author specifically mentions reverse osmosis.

He also covers multi-stage stills:

> My garage demo has very little going for it in terms of efficiency. It’s about as basic as distillation gets. There’s lost heat going everywhere. Modern distillation setups are much more efficient at separating liquids, especially because they can take advantage of waste heat. In fact they are often co-located with coal or gas-fired power plants for this exact reason. And there’s a lot of technology just in minimizing the energy consumption of distillation, including reuse of the heat released during condensation, using stages to evaporate liquids more efficiently, and using pumps to lower the pressure and encourage further evaporation through mechanical means.

Yes, RO is energetically the best, but places with geothermal excess, like iceland might choose the heat based method as they have free heat = the still warm water discharged after power still is warm enough for distillation.