Nah but seriously, I think the "rat" in mall rat means the same thing as in gym rat. A person who goes there a lot. Keeping in mind that Americans use the word mall for what many others would call a shopping centre. Google says
a young person who frequents shopping malls, usually for social purposes.
Then you can just have mall rat, gym rat and 2 other places people frequent like park rat or cinema rat or something. My complaint wa sjust that I have never heard of the term and don't think it's widely used.
Both of the two that they actually used are reasonably commonly used. Enough to have entries in dictionaries for them and movies named for them. The examples you gave are not ones I've ever heard, and I doubt they're used.