Core gaming would be gaming a good amount of time, and doing so with challenging games (doesn't have to be the epitome of difficulty but it should have some good challenge).

Agreed. nothing wrong in liking those games, but they don't make anyone hardcore.

Probably the most accurate description of a core game in the thread. Core gaming comes down to the game mechanics, not the number of sales, or the audience that plays it.

For me Core and Hardcore are different things

Core is the most mainstream games of the current industry, the base of the pyramid of the current industry, that would be Cod, Fifa, GTA, Skyrim and Assasins Creed.
That is why the Wii U does badly, Wii U is basically like having a diet without bread, that is why it is fine as a secondary console but few have only a Wii U.

Hardcore means games for gamers that have a taste that goes beyond the most popular and accesible titles.
Dwarf Fortress, the Souls games, Europa Universalis or Etryan Odyssey are more hardcore than the "core" titles I mentioned before.

Here's some core games.

Yes, core and hardcore has to be differentiated.

To make a comparisson with music: Beyoncé, as a random example, is a good quality music that many people like and that makes a lot of money - Core Music.

The Strokes, as a random example, may be better quality (top band in NME list http://www.nme.com/list/the-top-100-greatest-albums-of-the-decade/158049/page/10) but are less popular and makes less money - Hard Core Music.

PSY Gangnam Style, as another random example, is low quality music that generates sales but not much of lasting fan support - Casual Music.

this pretty much sums it all up.

My point was that the games are mainstream but the players are very serious about them and spend a lot of time on them that's why I can't define core gaming.

But I like this defininition "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."