A little more information is available. Here is a PDF from Los Alamos. A Green Freedom plant producing a million gallons of gasoline a day would cost about $5 billion to build, half of which is the nuke. The carbon dioxide in the air (about one part in 3,000) combines with potassium carbonate and water to produce potassium bicarbonate:
CO2 + H2O + K2CO3 –> 2(KHCO3)
Then the potassium bicarbonate is electrolyzed to extract the carbon dioxide, now concentrated. along with some hydrogen. The carbon dioxide and hydrogen are combined to make methanol, and the methanol is used to make gasoline. None of this is rocket science, and most of the pieces are available off the shelf. What is new here is the combination of the pieces of technology in a financially practical way.
Climate Progress calls it a new way to waste energy, and suggests that it would be much more efficient to use the nuclear power plants to run electric cars. Which is true, but the point of liquid fuels is not energy efficiency, but energy density, ease of refueling, and the existence of infrastructure.
Another criticism is that Green Freedom is too expensive… not true at all. That’s like saying if gas is worth $5 a gallon, we can’t afford to make it for $4.60 a gallon. The $4.60 already includes the cost of capital.
Green Freedom just might be part of the energy solution, maybe not here, but in countries less squeamish about nukes.
See also: