Yeah no not really. They don't conduct traffic stops and aren't charged with enforcing DWI laws. It's right there in your text, their job is to worry about "violations committed on or about alcoholic beverage control licensed premises" and that's what they are for.

Presumably they are sworn law enforcement officers, and as such have the technical ability to enforce the law generally, but it's really clear that the person in question has a job enforcing liquor license law, and was outside their normal job description on this one.

It's equivalent to a fish and game warden grabbing a shoplifter while at the mall. It's allowed and legal, but not normal.