Interesting. I have a two year old and he will often get my 3DS down and play Zelda for 5-10 minutes. He puts it down after that and show none of the behavior you observe. He may just be too young to have a long enough attention span to care. However- he gets very angry when he has to come inside- the longer he is allowed to play outside, the more angry he gets.
I read recently, maybe even on HN, an article suggesting that children under [i forget, 3? 5?] should not be exposed to 2d screens at all, because their neural model of the physical world is still in development. Food for thought.
Instead they should spend their life drawing on paper with crayons?
I'm not sure I hold this suggestion in that high a regard. It's odd that some of the most highly intelligent people around enjoy consumption of 2 dimensional art forms - graphic novels, comics, xkcd. So I'm not entirely sure that I can see how 2D screens would affect their abilities... and honestly, I didn't even make it out of 1 dimension. Comics never really did it for me. I never really graduated from regular words on a page, maybe a couple of pictures or diagrams thrown in :P
That said, there are some great educational shows on TV that I don't mind them watching every waking moment if they decide they want to (How It's Made, Mythbusters etc.) It's the mindless rubbish (and the advertising!!) that seems to cast a spell on them that I object to.
I've read some stuff about that, but haven't seen any strong evidence. My wife and I try to expose our son to a wide variety of experiences. If there is any strong research about this, I would certainly like to review it.