While I agree with the sentiment of "anyone can be a gamer", I wouldn't necessarily say that simply "playing a game" makes you a gamer, anymore than "watching a movie" makes you a film buff, or "playing a single round of golf" makes you a "golfer". These are descriptive labels for people into particular hobbies. it's okay to interact with a hobby without being very involved in it. Some people play games but aren't gamers, and that's okay.
IMO: if you're playing games regularly, are interested in games, are buying games or putting money into the hobby, or following gaming news, you're a gamer. It's not a high bar, it's just "you're into games".
My mom plays candy crush but she is not a gamer, nor would she call herself one. But some girl who spends a ton of time playing love nikki, or buying every otome game? definitely a gamer.