IMO one of the worst aspects of modern "gamer" culture is this insistence on purity tests particularly when they're aimed at games that are extremely popular with women.
Even in terms of market segmentation I don't think the distinction of "overall gaming fluency" is very measurable or meaningful.
You can't have the same conversation between someone who plays only candy crush, and someone who plays a wide variety of games. Its like saying that 8 billion people read books -- but 7.9 billion of that only read harry potter. Suddenly that 8 billion readers is far less notable.
There's a scale to your level of hobbyism -- a lot of people only play games as long as their friends do, because its simply a social tool (replacing the mall). The current flavor just happens to fall under video games, but theres no stickiness -- if the next popular thing is laser tag, they'll shift out and never think about games again.
The notion of trying to define this scale as a problem is also largely unique to gaming -- it exists elsewhere without issue. Painting, movies, programming, literature, music, engineering etc there's no issue saying that someone is dipping their toes into the subject, or has purely commercial interest in it (eg I only watch best selling movies, or only marvel) or has an actual interest in it (a -phile, a hacker, etc)
I think the key difference is the prevailing belief that there is no depth to this subject, so the only difference between a casual entrant and a hobbyist and a professional is an arbitrary checklist.
Obviously I disagree -- there is depth, and therefore, there is a difference between "gamers", as they fall between the ranks in understanding that depth. Ofc theres no great metric, and you can't define it in detail, but the difference between a candy-crush-only "gamer" and a genre-agnostic "gamer" and a genre-loving "gamer" and a read-the-literature (what little exists) "gamer" in recognizing and communicating about that depth is readily apparent
The problem mostly comes from people who define their hobby as their life. I play games a lot and make them professionally but wouldn’t call myself a gamer. I don’t see my wife playing Match-3 games on her phone as lesser than my wife playing Baldurs Gate. Likewise I can enjoy Sage Solitaire and Escape from Tarkov.
Gaming is mainstream now and people who feel threatened by that need to grow up.
It would be the difference of trying to communicate about movies between someone who has only ever seen marvel films, and someone who watched say the entirety of the criterion collection. Or the difference between technical sales and engineers. It'd be fairly meaningless to give them the same label -- one is clearly capable of a more advanced communication on the subject than the other, if only because they've experience a larger subset of the subject.
Of course, you could also play the living hell out of a single game and be extremely fluent about only that one game -- which is clearly different than someone being fluent about games in general. We wouldn't expect someone who only ever played SC2, even if he had put 2000 hours into it, to have anything notable to say about FPS games and RPGs.
As you've opined, the marker of when you'd be considered a "gamer" vs otherwise is an arbitrary meaningless distinction, a random line drawn in the sand, but that's why "fluency" is trying to be introduced as an alternative.