Something of note in the link is that the hydrogen is hypothesized to be the result of water-mineral reactions. As a kind-of chemist I'm skeptical that those reactions involve most rocks, which consist of silicates -- silicon-oxygen based minerals. Getting hydrogen out of water means that the oxygen has to react with something else. Compounds that ALREADY are formed of oxygen in combination with something else aren't going to work.
Anyone remember water gas? It was used around the turn of the 20th century before natural gas became available. It was made by passing steam over very hot coal AKA carbon. So one possible route for "white hydrogen" is the reaction between hot water and hot coal at great depth.
Water gas also contained carbon monoxide, highly toxic. My admittedly brief online search didn't reveal a strong relationship between white hydrogen and carbon monoxide, but slower reactions between water and coal at high pressures underground might favor the production of hydrogen and carbon dioxide instead of carbon monoxide. One method of capturing CO2 involves pumping it down into the ground where it supposedly reacts with "minerals" so it can't re-escape to the environment. So perhaps the carbon dioxide byproduct is "scrubbed" by the surrounding minerals. Being one of those who want to know, I have to wonder just exactly what minerals CO2 DOES react with in this scenario, since most minerals are relatively stable compounds and not easily persuaded to combine with something else.
More questions than answers.