Now, I'm impressed.
Naturally, the article and claims are mostly air without any details about the processes used and a link to some test results.
Perhaps they are using the CO2 produced by the ship engines along with hydrogen obtained through electrolysis or high temperature dissociation to feed some variation of the Fischer-Tropsch process to yield liquids. That does not sound like a more efficient substitute for simply carrying Jet A on board.
Now if you add a nuclear reactor to provide the needed energy (electrical and/or heat), then you may be able to see the claimed results. That might make sense for a flattop but would not have much use in a submarine. All the U.S. nuclear cruisers have long been retired, so I can't see where it would work for turbine or diesel craft.