DrHades, I really think your view that saying only "hello, gl" is rude, is an outlier here. The analogy to your little old lady scenario is if I say hello, and the other player says hello and then wants to chat about the game/strategy and I ignore them (which would be kind of rude). It's perfectly common to just pass your neighbors in the hallway and say hello and nothing else...
My view, for what it's worth...
Greeting: I almost always say something along the lines of "hi there, gl", unless I'm distracted at the beginning of the game and forget. If I forget, I'm not offended at all if the other person doesn't say anything. But, I do find it a little weird when I greet someone and they don't greet me back.
Conversation mid-game: I almost never talk, but don't mind chatting if the other person wants to.
GG: I am with olneyce and DsnowMan. In this community, it basically means, thanks for the game (I do like the Little League analogy too - even if you really hated to lose, you had to say good game...). So, I almost always say it. If I really trounce the other person, sometimes I'll say "thanks for the game" (recognizing that the other person might view "gg" as rubbing it in). If it actually was a particularly great game (maybe 5% of the time?) I will say something more to acknowledge that.