How does the score abstraction of "loot" fit into your taxonomy? Many games are built around using items as score.What do you meant by "loot"? Is that the meaning of the score which is used to represent an item?Sorry for my bad English.
My understanding of your definition of a game-score is: a abstract or concrete metric within a game.
I was missing items, such as gear and property (houses, decorations etc) in your list. Many players like to play game to get more items, or to get the best items.
Perhaps a player's item is not abstract enough and could be described with the terms in your taxonomy.