Of course, if the dehydrogenase actually refers to a blend of both alcohol dehydrogenase *and* acetaldehyde dehydrogenase, then they’d have a modestly useful product. Alcohol detoxification via these two enzymes does occur in the stom\ach (in men only - women lack the enzymes in their stomachs. Both genders, however, do the majority of metabolism in the liver. However, this difference is the reason why men can generallly drink more). Anyway, if you had a product containing both enzymes in
useful quantities, it would probably allow you to drink more Grange Hermitage than usual before leaving the pub for the night….Of course, as you’ve suggested, it’s more likely they’ve only included one of the dehydrogenase compounds.
Another possibility, rather than them having included alcohol dehydrogenase in their product, is if they’d included solely

aldehyde degrogenase instead. As it’s the acetaldehyde which makes you feel so awful when you’ve been drinking heavily, additional enzyme could at least help make you feel a it better. It would do nothing, though, to hasten the removal of alcohol from your blood stream per se. In any case, I’m not sure if this would be viable given that once alcohol has been metabolised to acetaldehyde in the liver, I don’t think gastric metabolism would play a major role in detoxifying acetaldehyde to acetic acid.
Bottom line: if someone can come up with a pill that contains both enzymes in useful quantities - I’d be willing to bet that
it would have some effect. That doesn’t seem to be the case here though, does it…