CA had commented on how rules effect the story that the PCs are in by altering it's tone. As he quoted "the medium is the message." Understanding how a rule alters the tone of game play is important for any designer to understand. I think a lot of times we design by saying I think this is cool. We may know a rule enhances a certain style of play instinctively, but what if there were other rules that would enhance the effect you're after?
Instead of saying "my game uses a dice pool." it would be so much more convincing to be able to explain why that's awesome.
There may be categories of rules that evoke a certain feel but I don't think we could pick that out of the air (maybe CA could he seems to have been thinking about this). So I'm thinking of just attacking this concept by concept and then maybe forming some structure later. Here are some examples of the thought process off the top of my head.
Additive Dice Pool - Gives the feeling of action. Lots of dice makes it seem like the roll is significant. Helps to evoke a active or momentous feeling.
Single die rolls - A simple action with a readily understood result. Important for when the results are intended to be arrived at quickly. Helps to make the roll the roll a low mental investment and faster feeling.
Opposed Dice Rolls - Sets up a direct conflict between characters. Gives the feeling of the players challenging other players (including the GM) directly.
I don't even know if I've got those right but it's a start. What kind of mechanic evokes what quality in your games?