It is grossly incorrect because it does not "produce oxygen from Martian soil".

This is extremely misleading, because on Mars Martian soil is abundant, while water is very scarce, so the title makes the reader believe that this cyanobacterium solves easily the production of oxygen.

It does not help at all for oxygen production. If you have water, then it is easy to produce hydrogen by electrolysis, using solar energy. Getting water on Mars is the hard problem.

There are chances that such cyanobacteria will be used on Mars, but for producing protein and other useful organic substances, with oxygen only as a byproduct.

However I believe that at least for the more distant future there is a better alternative to the use of cyanobacteria: the capture of solar energy by artificial means, coupled with the synthesis of some simple organic substance, e.g. glycerol or glycine, which can then be used to feed a culture of fungi located underground, which can then produce proteins and all the other complex substances needed for human food. There already are genetically modified fungi that can produce whey protein or chicken egg white protein suitable for human consumption.

This variant is better because photovoltaic cells have better efficiency for capturing solar energy and without environmental constraints, while genetically modified fungi can produce proteins of better quality than cyanobacteria and also any other complex organic substances that will be needed.