This inversion of the laws concerning the conservation of energy puzzled me as well.
Simply unlocking CO2 and hydrogen from seawater is highly energy-intensive, and it has to come from SOMEWHERE. CO2 and hydrogen CAN be turned into fuel, through something called the Fischer-Tropsch process, but to proceed on an efficient basis, it requires a relatively high temperature to assure the carbon dioxide transforms into carbon monoxide, then the reaction can continue in the direction of forming hydrocarbon fuels.
The chemistry has been widely studied for 80-some years, and was put to use by the Third Reich in its dying days, to supply fuel for the Wehrmacht, after they had been denied access to oil fields in Romania and elsewhere. But the Germans still had a lot of coal, which was their base resource, and the process of making “syngas” had been well established many years before.
THERE IS NO COAL FLOATING AROUND IN THE OCEAN, but there may be a lot of organic matter there, which would be the source of the carbon necessary to make the carbon monoxide feedstock. Water, of course, is composed of hydrogen and oxygen, but it still takes considerable power to unlock that source.