Well, I think I see the basic point: Diesel fuel is carbon and hydrogen. We can get the carbon from a theoretically 'bad' gas in the atmosphere and water is 'everywhere'. With just a few more million in research grants, we might find some magic solution to make it feasible.
Though at some point, it becomes more about the laws of physics rather than technology or economics. I already mentioned the first electrolysis step of the process isn't economically advantageous enough to allow hydrogen to be used as fuel... let alone considering the other two equally high-energy steps. If you look at it another way, the Fischer–Tropsch process is basically the last two steps of CO + H > HC + O2...that process is not terribly economically feasible even considering solid carbon / coal as a starting point.
Considering atmospheric CO2 is only 400ppm or 0.04% concentration. For comparison, argon is ~ 0.935% ...over 23 times more plentiful. I think my last argon for TIG shielding gas was ~$80 for 240cf cylinder. Even assuming CO2 costs the same to isolate, back of the envelope scratching shows a cubic foot of CO2 is about 52 grams in total, though that's about 14 grams of usable carbon and 38 grams of 'useless' oxygen. That $80 gets you a little less than 7.5 lbs of carbon... pretty expensive chunk of coal.
Unfortunately, I think articles like are more common than ever, but are more about free publicity for the company, a source of 'feel good news', and a plea for more research funds than they are about any true technological breakthrough, or technology which will help the 'real world' anytime soon. But who knows... we can always dream ...and pay for more research.