Glutathione is something that the body manufactures (endogenous) as opposed to ingests from the outside world (exogenous). Glutathione is an anti-oxidant used in cells to neutralize free radicals/reactive oxygen species. The paper is a 'hypothesis'. One of a gazillion currently proposed.
Supplementation of other anti-oxidants has largely shown to be harmful. Supplements in general are not useful for the general population. If one has specific deficiencies then yes as treatment. Randomized trials of oral glutathione supplementation have been negative to improve oxidative stress biomarkers or glutathione levels - glutathione is a tripeptide (small protein) and is likely mainly digested. A glutathione precursor, N-acetlycysteine (Mucomyst) is used in cases of acetaminophen overdose. Acetaminophen is very deadly to the liver (and thus the body) when excess is taken and excess is not dramatically more than the therapeutic dose.