STALKER is most certainly a shooter.
Thing is (at least this is my perception), it's not designed to be one of those typical action-packed FPS games that we're all getting tired of.
Maybe it's because it isn't very GOOD at being a shooter (above I said I think some of the flaws of the game give it its charm... this would be one example), but I don't believe they tried to make it a GOOD one.
Toss in some weak RPG elements, some really neat game mechanics and ideas (that still need ironing), and some atmosphere that at times is almost tangible, and you got yourself what I consider a very unique game and experience. It's set up in such a way that you know you are in trouble if you aren't careful. The setting is intimidating. You don't control it, and it couldn't care less about you. I had the same feeling while playing games like Daggerfall and Fallout.
It's like they threw you into the Zone, gave you a gun, and said "You are going to need this if you're going to explore and live in this environment. It'll be clunky, it won't be too reliable, and you will likely die many times. Survive. Enjoy."
Granted that feeling goes away once you get overpowered, but it keeps dragging me back, finding mods to enhance this feeling and making it more difficult to the point where every bullet counts and if you miss a shot, you will likely end up dead. I find it convincing every single time I play either game.