Things that sound too good to be true usually are. The quoted part of the story says ships wouldn't need to be retrofitted to burn it, not make it. Two things strike me about the method, one is that getting enough dissolved CO2 out of the seawater to do this would require processing very large amounts of seawater for each gallon make, and that doing anything chemically with CO2 normally requires huge energy inputs, on a scale that only the reactors in the carriers could be used for practically.
I'm pretty skeptical, of course it'd still be cheaper than the $50+ per gallon actual cost for biofuel that the Navy is currently being forced to buy and use in large quantities in order to support political causes, donors, and bundlers.