This question is really dumb. Yes they are and that's that. Why wouldn't they be? Also, every console has plenty of core games available.

What I can't understand.(though i think you are right)

Without consoles there would be no AAA games for pc gamers as most of them simply don't buy games to finance big budget projects-just copying(diablo and sim city are no aaa games but aaa bugs)

I mean I don't doubt that they are the arian royal overlords but acting like a sponger  is a strange behaviour for a master race.

Are only those who pay the games our masters,or the steam fanboys or those with intel cpu's or anyone who ownes a pc?(than i'm part of the master race,but I don't want to)

Yes. If you have 360 or PS3 you're getting 90% of the "core releases". Most PS3 exclusives, Halo, Gears, Forza, and L4D are all core games I'd say. I also consider Mario, Zelda, SSB, and DKC to be core but you don't have to play every core game to be a core gamer. I mean I'm just not interested in enough of the 360 games to buy one but I don't think I'm casual because of that.

I can prove your definition is wrong.

I'm just a core gamer playing less than 15 hours a week but I am/was?(haven't watched the charts for weeks) world no.1 in two pinball arcade pinballs without investing much time(th. of magic,twilight zone)like a hardcore gamer.

On the other hand I'm the worst shoot'em'up gamer i know-no matter how much I play I stay on a very low level ,even from a casual gamers point of view I play like a noob.seems i have no talent for this kind of genre though I like it very much.

This has nothing to do with the thread, but who is that on your profile pic.

Depends on how that gamer feel about gaming..I guess

I don't think it's a matter of console so much a matter of the games. Say if someone only owns a 360 and plays games like Halo, Gears of War, Fable, Alan Wake, Bioshock, Dragon Age, etc for a fews hours a day, I would consider them a core gamer. Now say if someone else owns a Wii, PS3, and 3DS and only plays Mario Tennis, that brain puzzle game (can't think of the name), and LBP Karting for like 10 minutes every other week, I wouldn't consider that person a core gamer.

Can a surfer only have one brand of surf board and still be a surfer?

Of course. Some of us barely have time to play 1 console. let alone 3.

These threads are a little confusing and quite redundant.

Question: Do I consider single system gamers core gamers?
Answer: If they are core gamers, then yes.

People can be core gamers even if they only play one system, just like they can be core gamers and favor any of the big three console manufacturers or favor PC or another form of gaming. You could potentially own multiple game systems, and a gaming PC and not be a core gamer (this was me during college, just didn't have time for it). It's also not dependent on what kinds of games the person plays as long as gaming is a large-scale hobby for them.

For example, my sister is someone I would not consider a core gamer. She does enjoy some gaming and at times (notably during our mutual childhood with out SNES and GBCs and later my PS1 and then a few years ago when I gave her my old DS) but does not put nearly as large of a time investment into as I do most of the time. That being said I have seen her beat Super Mario World levels and navigate the Legend of Zelda like a pro, she beat Final Fantasy IX when I couldn't stomach the changes from VIII, she got her copy of Pokemon Red beat before I could beat Blue and actually convinced me to try out a Ace Attorney game (I knew of them but had never taken the plung)

On the other hand is my cousin, she I would consider a core gamer. From a very young age she has always played lots of video games (even more than me which is quite an anomaly in my family). She is a year younger than and had an N64 during the time I had a PS1, then during the PS2 era when I abandonded consoles for a time she had her PS2 and kept harping on me for not playing the RPGs and all the other great games of the period, and for the past few years she has been a pretty big XBox gamer, playing both Rock Band and Left 4 Dead competitively at time. She now is pretty heavy going to school, just had her first kid and got married, but still finds time to pretty agressively play or atleast be aware of just about every iPhone and Android game that comes out, letting me know about some of the gems that come along. So even though she doesn't play PC or really much on consoles anymore (and unfortunatley probably won't be able to for most of the next gen) I would say her dedication, the amount of time and effort, her passion and knowledge for gaming mark her as a core gamer despite the type of game she is currently mostly playing.

Long story short - you are asking if one group of people (based on an arbitrary defining characteristic) are all something else only partially related, it is generalizing and will always produce fallacy.