It isn't impossible to be a hardcore gamer, what makes it different from anything else? There are people who play games for a living. Seriously, check out the pro-gaming StarCraft community, it's massive in some counties, so massive that the gamers themselves have to be able to make between 200-300 actions a minute just to be able to compete on a decent level. That is something that is applicable in the real world, as it would be very helpful in a desk job to type quickly. These people also acquire rather huge pay checks, yet you call them childish.
Correct. While I am certainly not the best gamer in the world, I have played different games at different levels. Here are some and how I would classify them (and the games I've played at different levels).
Professional: (None): Full sponsorship and income, ie Evil Geniuses (EG) sponsoring Idra in Starcraft 2. The sponsoring company often sends the players to LANs to represent them and compete.
Semi-Professional (Team Fortress 2): Some form of significant prize or monetary worth generated when played at a competitive level. Played online and won prizes at major LANs that I sold for cash.
Competitive (Quake Live, Pokemon, League of Legends, Starcraft 2): Playing seriously against other competitive players/teams in organised play.
Serious (Legend of Zelda, Portal, Age of Empires 2): Playing with a greater intensity than most, ie 100% clears, etc. Often players are restricted from playing at a higher level due to the nature of the game (may often find ways to take it further ie ranked speedruns).
Casual (Minecraft): Playing occasionally or simply for the fun of it, not taking the game too seriously.
I avoid the term 'hardcore' as while it may once have kept its intended meaning it has been warped by the crowd that we all know shames its name. For such gamers I leave them in casual. Let me know what you think (obviously there is overlap, ie a professional gamer is a competitive and serious gamer).
It should be noted that the type of gamer is not related to the type of game. Often people classify games such as Farmville as casual games but that does not mean all players of Farmville are casual gamers.