What an interesting question!
I think in many ways, hardcore gamer is like a badge. People wear it to be "cool". Most people talk about themselves as hardcore gamer with a slight sense of prestige. It's a badge to keep "uncool, lame casual player" out of our little cliquish circle. It's another way to be special.
To be honest, I despise the "title". I rarely call myself hardcore. I'm a gamer, plain and simple, I play game, I play console, I play PC, I play mobile, I play "lame" facebook games, I play "housewife's favorite" hidden object games...
However, that being said, from a research and statistics perspective, we have to be able to separate gamers into different segments, so we can better understand them, their gaming behavior, their taste towards different genre, and of course, their spending habit.
So we normally separate gamers into 3 segments: Casual gamers, Midcore gamers, and Hardcore gamers.
One of the most important features to separate these 3 is their play time and the length of each play session. In other words, how long they spend playing game in a given period of time (a day, a week, a month), and how long they spend continuously playing game.
Casual gamers tent do have shorter play session and shorter play time over all. They play facebook games and mobile games, most features short play sessions, 3-5 minutes for facebook games, 5-10 minutes for many mobile games*.
Hardcore gamers plays longer sessions, often hours; and their total play time are a LOT longer, easily above 10 hours each week. They play on console, on PC, and often with bunch of friends playing multiplayer online. These kind of play style often requires player to set aside several hours, sit in front of TV or monitor, completely focused on missions/matches at hand.
Hardcore gamers take pride at what they do in game. They're proud about their in game achievement, their multiplayer rank, their virtual reputation in a MMO community. Gaming is part of their individual identity. They talk about their game character as if talking about themselves. For example, when I talk about my FemShap, I rarely say her name, I almost always say: "So I went to Omega and guess what, I met Garrus there!" Hardcore gamers identify themselves with their player character, they're emotionally attached to the characters, even sometimes they don't admit it. That's why when studio screw up a game, player are so angry about it (Mass Effect 3 Ending outrage). Many are heavily involved in the cos-play scene, even more identified with their beloved game characters**.
From this perspective, Hardcore gamers are still traditional console and PC gamers. They're somewhere between 18 - 35 (however the mass population is somewhere around 23-30 young working professionals). This person have about 70% chance to be male. Depends on genre, that percentage could be a lot lower*. This person is most likely a college student or young professional with steady income (games are not cheap, consoles are expensive, video card and gaming PCs require some serious investments). This person would spend a lot of time playing games, most likely with friends. He has long play sessions, often last for hours. He most likely own both PC and console, but often have primary gaming device. He's passionate about game, he's involved in online forums, spend time discussing his game with other people. He has a few friends he'd play game with regularly.
As much as I'm optimistic about the future of mobile game, I don't think we'll change the definition of hardcore gamers anytime soon. they're many "hardcore" mobile games out there. However due to the "handhold" nature of mobile and people's playing habit (waiting for bus, in transit, lunch break) people tent to play mobile games in fragmented time, in shorter sessions. There's not much to "identify with" without a compelling story, well developed characters. Mobile gamers pick up the game and drop it when they're ready to get off the train. It's still a pass time, not something you're passionate about (to the point of crying or rage). Very few people think about peas and zombies after they stop playing PvZ. But many think about Master Chief and Cortana months even years after they play Halo. It's hard to have some life shattering moments with angry bird, but many had been shocked by games like Bioshock, or Spec Ops: the Line.
I'm not saying mobile can't provide this kind of experience, but it's very unlikely a developer would create a heavy mobile games simply because current mobile game play behavior doesn't favor that kind of style. You could be in the middle of a important cut scene, and your doctor is ready to see you, break the immersion, and the magic of the game is lost. Player don't want that, and developer won't want it either. Instead, there'll be more and more "pick up and drop it" games features lighthearted theme and short play sessions, which firmly put mobile game in the "casual" category.