You'll likely find many perspectives of what's meant by "gamer".
In general, I find the term mostly fitting to people to whom gaming has had a large impact on their life and/or leisure time. That means as a collective you share certain experiences that bind you together, though obviously it's more divided into certain major clusters of categories. You could also be a mobile gamer then and share some experiences that other clusters of gamers don't get, but other people into mobile gaming recognize and empathize with. You might belong to many of these categories, recognizing experiences from many types of gamers. There's also a large element of time and age cohort, especially related to childhood and adolescence, where the experience of gaming and a community of gamers is deeply connected to being a part of that history, of growing up with generations of games.
That's how you'll also see large gaps in regards to a community of gamers, depending on what they grew up with, to whom they'll be able to share a sense of community with. It's a historical phenomenon, deeply connected to a sense of community in shared experiences.
