There are two ways of understanding the relationship between games and representation:
Games can represent (they contain internal depictions)
Games are representations (a game as a whole is a sign)
Meaning in a game emerges from the interaction between system and context:
The system of a game's meaning is the set of formal relationships defined by the rules. It is the pre-existing structure of signs that does not change from game to game.
The context of a game's meaning is the space of experience where interpretation takes place. Interpretation in games is the act of play.
This process of generating meaning is not unique to games. For example, meaning in language also emerges from the relationship between formal systems (grammar) and the context of interpretation.
Because games are emergent systems, even a simple system can generate infinite meanings. The resulting set of possible meanings is the space of representational possibility of a game.
Players in a game navigate this space of representational possibility through interaction. Game designers, by creating chains of actions and outcomes, build this space of possible meaning.
The magic circle of a game is the space where special meanings obtain. It is the space where the rules of a game take hold, as well as the context for the interpretation of meaning.
The meanings within the magic circle of a game are derived both from the internal formal system of the game as well as the ways that the game refers to the real world.
A cognitive frame is a way of organizing how we look at the world. Game players take on a cognitive frame that affects how they interpret actions and events.
Metacommunication is communication that takes place in the context of play. In addition to communicating game actions, players are also always communicating the fact that they are "just playing".
Metacommunication helps generate the complex play of meaning in a game. Every game behavior signifies an action ("I just captured you!") but it also signifies what the action is not ("I didn't really capture you, since we were just playing.").