It's a first law of thermodynamics certainty that it takes more energy than it produces.
The only thing this might be useful for is to store energy from intermittent sources such as wind and solar in the form of hydrogen for future use.
It would be pointless to use fossil fuel electricity for this process, unless the hydrogen itself is the desirable end product for use in hydrogen-fueled vehicles. But even then, it is more efficient to derive hydrogen from natural gas than it is from the electrolysis of sea water.
You are exactly correct and if the person who wrote the original article was even minimally competent, that’s what the focus of the article should have been.
If one is worried about CO2 emissions (I’m not), the major problem with windmills and solar panels is their intermittent nature - even if you overbuild by a factor of 5 or 10 relative to carbon fuel sources, on a still night with heaters or air conditioners running, you’re ‘sh*t outta luck’ if you don’t have back-up for those systems. Adequate battery back-up is prohibitively expensive (at least for now), so storing excess wind/solar electricity as chemical energy (that is, H2 and O2 in this case) could be of value.
Except electrolysis has pretty poor efficiency, and storing H2 is problematic. This article explores a modest technical improvement in the electrolysis process (and most technology advances in such small steps) - but as others have noted, it’s no breakthrough and far from any panacea.
Technically that’s the 2nd Law. 1st Law says the best you can do is break even, 2nd says you can’t even do that.