I've been making a point lately to try out a test, effectively it goes like this:

If two games are equally highly reviewed, 3D World and GTA for example, then the more core one is the one with less mass-market penetration. - The same argument could even be made for the Wii-U and Vita against their more successful rivals from each other's company.

This seems to upset people because 'core gaming' is apparently associated with 'higher quality' which isn't always true, I've picked a 3DS over a Vita due to personal taste and I'm an indie developer (sorta, none of my projects are launched yet) so I am definitely a part of the core market. That, however, does not mean I can deny that people who have the Vita are more likely, on average, to have an interest in gaming comparable to mine.

You could even cite the success of good indie games on Wii-U and Vita as a partial demonstration of this, so is it not the logical business view? What definitions do you use?

someone whose main hobby is gaming, that plays a lot of games in wide range of genres, and follows gaming industry news on a regular bases.

A core game is a game that requires a high level of gaming experience and knowledge. Journey is a core game because it's entire development is built around the idea that someone is at least intermediate when it comes to video game experience. Dark Souls is core because in order to play it successfully, you must have an intermediate experience with games.

Neither 3D World or GTA V are core games. They are casual games with core appeal. That's why most indies are core games. It's all about the expected knowledge level.

It has nothing to do with quality, though.

Most of the time, when people talk about "hardcore games," what they really mean is "western style games who's target audiences are people over 15.

...And JRPGs."

Anyone who plays video games for several hours weekly or so is a core gamer in my book. Doesn't matter if they play Minecraft, Calladooty, Hello Kitty, Super Mario, Angry Birds or The Sims. Hell, even if they only have an iPhone and still enjoy games as one of their main hobbies, they are core gamers imo. Core Gaming is nothing but love for games. Which games exactly are played is purely up to personal taste.

Your definition also makes sense to me. It feels more gamer centric than the business centric definition I gravitated towards. - Can we pretend it was the unnoticed clash of those two definitions that create this whole mess around the term?

To me overly successful games - as mature, violent, deep, entertaining they may be - are never "core" games.

I avoid the terms core and casual but when a game is known to every and any gamer and even people who do not play video games, that game can only be casual in my eyes, as in people (lots of them) just play it occasionally/casually.

Core games - as in "only the core of gamers plays this" or "only for hardcore players" (I think games are for anyone but this is how I interpret the core/casual debate) - are complex, difficult, hard to get into material. There's crazy debates about whether video games are art but in this case I like to compare it to other forms of art. There's the mass (pop) market and art that doesn't fit there and therefore doesn't "succeed" the way business works. That's what core (odd, forward-thinking, innovative)/casual (mass market, polished, known mechanics) should suggest in my opinion. Mostly, it's the other way around, though, because people feel insulted when they play a "casual" game so GTA or Dragon Age would never ever be a casual game, of course.

To write even more: I love the Mario Kart series. To me, it's a casual game series because it's easy for everyone. I got into competitive gaming with that series and won multiple national tournaments, becoming a well-known player in the "core" community. Lots of people say (and keep saying) that MK Wii was the best in terms of competitive gameplay and balance. But in the end, it was just the most successful game because it didn't have complex techniques to be way faster than other players. When I tell people that Wii was the most casual game in the series they go all nuts because why would they like a casual game, of course it was the most core game of the series. I haven't read/heard any real argument why Mario Kart Wii is the most core, just that it is and it is just because.

Generally, I agree with this:

or games they are good at themselves.

I don't label games themselves as 'core', but I may describe some genres as 'hardcore'.

A core video game player is someone who plays a fair amount of video games, especially on consoles and PCs.
A hardcore gamer spends quite a lot of their time playing games. Generally more so than other activities, and they may binge on and can be associated with MMO's, MOBA's, FPSs, fighters, and even sports games.

Your question is confusing.  Are you talking about the core gamers or the core games they play?  Let me answer both.  And i will also be assuming you mean "Hard' Core Game/r.

Core Games--There are two ways a game is a core game.  Either they begin life as such, or they become core games.  Let's take Resident Evil 5 as an example.  From the very first announcement that this game is in production, it was considered a core game title. Why?  Because it had pedigree.  Capcom, Nintendo, Sony, Microsoft, Sega, it's a series title, it's predecessors sold hella, movies, action figures, accolades for miles.  The devolpers knowing this, and the fans knowing this, it's an instant core game.  The game may reach mediocre sales and bad reviews, but by rule of literal, the game is a core game.

A game that may become a core game is one that the gaming community dubs a core game--meaning that the status of "Core" is received.  For instance the original Donkey Kong.  It had no pedigree to speak of, no specific demographic, no prior installment to fall back on, just simply a game that became a core game by the whims of what the core gaming community had bestowed to it.  Tetris is another example of this happening.  What was tetris made for but just a puzzle game.  It became a core game when the community of gamers saw far more than what the game was, and it became what it is.  We can take a game like candy crush and look down at it as nothing more than a cash cow.  But what happens when there are gamers who are smart enough to make the game count.  By that, I mean it becomes more than a time consumer, perhaps the best players in the world are competeting for the best record.  Yet, Candy Crush is not a core game.  Why?  Because the overall consensus by the gaming community is that Candy Crush is not a core game. 

Core Gamer--This one follows along with a game being a core game or not.  That is because Core Gamers decide what core games are. 

First off, i just want to say, to be a core gamer, you don't have to play games all the time.  There's a difference between bieing a gamer and being an addict.  Addiction does not equal Core Gamer.  There are requirements to be a core gamer. 

1.  You must want to play games.  You don't have to play everyday, but you want to play games in the future.  There must be an emphasis on having the urge to play games.   Me, knowing that Star Fox is coming out this year and wanting to buy that game and play it, makes me core.  I may not want to play games everyday, but I will want to play more. 

2.  You must be knowledgeable about games.  You may want to play games and you may buy games all the time, but you're not a core gamer if you are not a knowledgeable gamer.  A gamer who games every game, is not a core gamer, that again is just addiction.  Think about voting.  Does the voter become a expert politician just by merit of voiting, or are they just some participants in an action.  That in turn can be applied to gamers.  Does the 11 year old cousin who is great at Call of duty a core gamer, or a casual participant in the action of playing call of duty.  Core gamers know about games and that's a credit to core gamers.  You may not know everything in the world about games, but you are a gamer who can put a good understanding of what a game is in other context than what is presented on screen.  Sorry, but you're 11 year old cousing killing me at Call of duty is not a core gamer.  He's still a gamer, but not a core gamer.  They may be calling me a noob at that game, but overall gaming, they're the noobs.  And until they have more knowledge gaming, they'll only be gamers. 

and...that's it, I guess.  If I'm missing something, please fill me in at what I may have gotten wrong. 

core gamers are people who spend more than they should on video games. the term is marketing speak made up by greedy publishers who want you to part with ever larger amounts of your money.

the whole (core) gamer identity bothers me a little bit. you shouldn't have to join a subculture to play a game.

I don't know, games like FIFA and Call of Duty are very mainstream but the gamers who play those games play them a lot.