Electrolysis is easy enough, and there's plenty of places with enough water.
Then you have hydrogen. Hydrogen is not nice to work with, store or use, so you want to turn it into something else a bit nicer.
The problem is, almost all practically usable liquid or gaseous fuels contain carbon. Where do you get that from?
The obvious answer is the atmosphere. That's also the premise of carbon sequestration. The problem is that CO2 isn't actually particularly abundant. It's currently hovering around 400 parts per million - that's about 0.04% of air. To make a kg of hydrocarbon you need to process an awful lot of air to get enough CO2. That all takes energy. A lot of energy. Suddenly your round trip efficiency is practically zero. If these guys have cracked that problem, it would be fantastic. I hope they have, but I suspect they haven't.