While the term used to refer to a gambler, "gamer" came to refer to a video game hobbyist. In recent years however, the term has been politicized. "Gamer" became something of a pejorative to many on the Left in particular as denouncing "gamers" became a means of signalling political allegiance. Those who disparage the term claim that identifying as a "gamer" is just tying one's identity to the products one consumes (because free games and emulation totally do not exist). Those types are often the ones who cannot imagine how anyone could to tie their identity to anything other than one's sex life or gender.
Labels for those who enjoy particular hobbies is not that unusual. Some terms that come to mind are: cinemaphile, bookworm, rock hound (stone collector), philatelist (stamp collector), numismatist (coin collector), gearhead, motorhead, railfan, trainspotter, foodie, outdoorsman et cetera. Keeping those other terms in mind, "gamer" is not really out of place. Especially when one considers how those who bewray the term often big fans of Harry Potter and the like. There is also a level of irony to the term "gamer" that came about when companies started using the identity for marketing.
I guess I am not too bothered by the term, but I am likely in the minority in that regard.