I used to have a problem with this term as well. My current understanding is that people usually use it to denote things in games that are due to clumsiness or laziness that we've just gotten used to because it's videogamez.
A good example would be force field walls in God of War or Devil May Cry, the ones that pop up when you enter a combat encounter, and don't disappear until you leave. There's practically no story motivation for these arbitrary walls, but the designers need you to stay in these areas. Not only does this force you to fight the enemies, but it prevents you from running away from them into a new area where there are more enemies: if the enemies from the previous encounter and the ones from the next encounter were alive at the same time, the game could go over its processing and memory budget.
What the force fields accomplish is called "gating." It's gamey because it's a clumsy and arbitrary solution that doesn't make much sense in the game world. Gating can be done a lot more gracefully: the Uncharted series has a handy way of doing this because more often than not you are accompanied by an AI companion. As you go through and play those games, you'll notice that there are a lot of doors that you need your AI buddy to open, like here:
http://www.youtube.com/watch?v=Kj76J...elated#t=1m41s . What you won't notice when you play the game normally, is that they won't help you open the door until all the enemies are dead. This accomplishes the same thing as the GoW force field walls, but in a way that makes more logical sense in the game world, is less obtrusive, and therefore less "gamey."
So yes, I, like you, love games that are straight up and honest about being games, and so it used to bother me that "gamey" was a pejorative term, but now I see how there are a lot of "gamey" design choices that are made unconsciously, and efforts should be made to avoid them if we wish to improve the state of the art.