Like my opinion of what makes someone an otaku (someone that has watched more than all the mainstream stuff and actually takes the time to branch out, along with watching more than at least 50 animes), a gamer is someone that has played a variety of games and got some progress in each of them (not downloading and saying "ugh the character customization sucks" and refusing to play cause of that fact). Only playing cod for all of your life doesn't make you a gamer, you just play cod and is really good at it (maybe, seeing if you play it for most your life it would force some skill into you, right?) Biting your Xbox controller in slutty clothes and posting it on Instagram saying "playing some overwatch, gamer girls exist ya know" is not being a gamer. You are just cringey. You most likely dont even know how to play overwatch. Platforms are another thing. If you take the time to save up for them expensive ass games and console, then yeah probably you are a gamer. But they dont really matter. Cant afford one? Ok, you can be a gamer with only your computer, it's fine.
Well, this is just my opinion. But, if you haven't had at least one round of Wii sports, are you even a gamer?