They are talking about turning CO2 into burnable fuel, so it's hard to see how this on its own would reduce emissions if you burn that fuel outside closed containers.
If 100% of the fuel we use comes from this technique - where it is imbued with carbon that was atmosphere-bound (flue gas) then we have decreased emissions significantly, since the alternative was that we release the flue gas CO2 AND the burning fuel CO2.
so long as it is a closed cycle it is neutral. That is the key. carbon from the air that goes back into the air is fine. Carbon from the ground that goes into the air is unsustainable.