It's an improved Fischer–Tropsch process. The same process Germany used to make avgas from coal during WWII. Apparently it is around 70% energy efficient and only need water (for the hydrogen) and air (for the carbon).
That seems dubious to me - they don't say where they are getting the CO2, but you're saying they extract from the air? The concentration of CO2 in air is still pretty low, I mean, air is what, 78% Nitrogen, and they don't even use it as a source for Nitrogen when making fertilizer. I would think there have got to be some materials high in carbon and some chemical reaction could be employed on that material that would liberate CO2 as a byproduct.
You mentioned making avgas from coal - that's probably where the carbon came from, not air.