What set of attributes can be used to describe, compare and contrast various board games?
Attributes that I use to evaluate games:


Replay value (Over time how much do you enjoy it)
Randomness (how much it's out of your hand)
Learning curve
What kind of skill does it require (strategy, resource management, deductions, spatial orientation, etc)
Time required to set it up
Expected time to have a game
Time-ness (is it per turn? all at the same time? you bid for who to be first?)
Degree of interaction (it's similar to what you say but it includes more things. Games like Bingo are outside of your scale)
Handicap-aware (How does it react to players with different levels. Is it easy for a newbie to give by accident the game to another player?)