Traditional arts is the best way to start on a concept artists path, not doubts about that. And there are most certainly jobs in the larger game studios for dedicated conceptors (I invent words, it's a bad habit) where they can move you from project to project, and of course there are studios like Massive Black. But like I said, to get in the door you need the full package, as many skills as will fit on a resume and demo reel.
Do you have access to a painting program? Photoshop or Painter or something? If you do, I'd like to see you post something.
"Fear is the death of courage"