I would say no. While I technically play video games, I do not play them very often (probably no more than 2 hours a week) and they're not the go-to thing I do in my free time. I'd argue playing video games doesn't make someone a gamer as "gamer" is something people actively identify with. Most people listen to music, but not everyone is a "music enthusiast".
There's been a lot of discourse over whether video games are bad or not. This article is mostly me rambling my own thoughts, it's not to defend one side or the other.
A lot of people argue video games are bad because they're a waste of time. Though I do not agree with this. I do think video games are unproductive, but most hobbies are unproductive because a hobby by definition is something you do for fun. Most people who play sports will not become professional athletes, but I'd never argue sports are a waste of time.
I used to be one of those people obsessed with productivity, but ironically, that attitude didn't make me more productive, just more stressed. Some people will try and make their gaming sound productive by saying stuff like "it improves hand-eye coordination" and "i'm building social skills", but be honest, is that really why you're playing?
If you think gaming isn't a problem, why not just say "I play video games because I enjoy them"?
While I don't think video games are a waste of time, I do have a problem with the way some gamers respond to non-gamers who criticise gaming. Instead of civilly disagreeing with them, they get very defensive.
Quite a few people have made YouTube videos about why they quit video games. In the case of Cam (from Game Quitters), he didn't quit because Andrew Tate told him video games are for losers. He quit because he was a serious addict and the addiction was ruining his life. It's clear his story is a testimony to people who may be going through a similar thing.
Despite that, a lot of people just interpret these videos as "GAMING = BAD!" and defensively say things like "video games are fine in moderation", "i'm gonna keep playing anyway" (bruh no one is stopping you), and "it's okay to play 1 hour a day". Would you tell a recovering alcoholic that alcohol isn't bad just because you're not an alcoholic?
While I could make time to play, gaming is a low priority because I have other hobbies/errands like going to the gym and making videos (which involves many steps like writing, narration, transcoding, editing, thumbnails, subtitles etc).
Video games can be quite expensive. Of course, this depends on the individual game (a AAA game could cost $60 while a 2D indie game might be $3), but with things like Steam sales, it's tempting to buy games just because they're on sale.
My Steam library is full of games I'm not really interested in, but impulsively bought when I was a teenager who lacked financial literacy. The worst part is I can't sell them or even give them to a friend who would play them. Since I'm now an adult with bills and financial goals, I can't afford to be that impulsive.
A few people have spoken about gaming not being fun anymore, and a common response is "Actually, gaming is still fun! You just keep playing the same games". For some people that may be true (I've met people who only play Minecraft and GTA V), but that's not the case for everyone.
As people get older, they may get into other hobbies. Whether it's fishing, BMX, or making music, I think people shouldn't try to hold onto something they're no longer interested in.