TFA was points to a 2012 press release, but it contains not much more information. They must need to supply energy to this reaction, but whether this energy is as heat, electricity or something else is unclear.
I see two uses from the point of view of the U.S. navy. One is to put one of these chemical plants in an aircraft carrier, power it with the carrier's reactor, and generate fuel for the aircraft on board. The other is to put the chemical plant on a nuclear powered supply ship, which will then transfer the fuel to non-nuclear surface ships.
From a world energy point of view, this is a way to turn non-fossil fuel power (nuclear, hydro, wind) into hydrocarbon fuel, with the overall process being carbon neutral. Burning fossil fuels to provide the energy for this process would certainly be counter productive in terms of CO2 emission and very likely economically counter productive as you'd be better chemically processing your fossil fuel instead.
By the time you're going to all of this trouble to turn electricity into fuel, it is unlikely that you'd want to run a car on it - you'd rather just have an electric car. For aircraft we really have no good alternative to hydrocarbon fuels, so it could be used here. However, on the road to a low-carbon future, we have decades worth of lower hanging fruit (notably coal power stations) before we really need to care about whether our aircraft fuels are carbon neutral.
Conspicuously missing from the articles is the energy efficiency of this process. Given the $3-$6 per gallon projected jet fuel cost, presumably the efficiency is not too bad. (I notice this number hasn't changed since 2012 which makes me suspicious that it is more guesswork than calculation.)