If by your definition of 'gamer' we have to be free-going balls to the wall playstyle, do whatever we want, and then brag how we did such and such solo, then obviously I'm not a gamer, at least during my MMO times. Then again, saying someone who plays MMORPG's is not a gamer, when the term game is in the acronym, then what are we, cus we sure are playing one, and remember, if it ain't your style, it doesn't mean its not still under the gamer category.
Then again, by this definition, a gamer is someone who plays entirely for themselves, and not by actually working with others towards a larger goal that is more than myself. Sure it may be cool and 'hardcore' gamer that you can get 20 man kill sprees on COD and do devil mode on DMC, but how is this not as bad as those who study a particular encounter and then have to manage and lead 50-100+ people to do an encounter? I'd personally say the latter has more to brag about, and forget the study part, its the managing so many people over voice, which can easily be disrupted by people talking out of place.(and as for those vent MOTD, those generally apply to the channels raids are taking place, free to chat in general ones)
You also may want to stop focusing on the proverbial 'hardcore' of the mmo people, not all spend days on end studying instances and cursing out people for not playing inside their part o the sandbox, some of us do play for laughs and have random events on whims.
As for myself, I do a bit of all aspect, I do the COD/Halo twitch moments and go rabble rabble now n then over my streaks of awesome, and then I also go on MMO's and help shape big events. In the end I can sure say that I don't feel any less the gamer when I do either.