Medium: a means or instrumentality for storing or communicating information.
The more of a story a game is presenting the more it is a medium, no matter how much of your interaction changes the story. You just become part of the process of being the medium. Much like being an actor in a movie.
Person A plays a game. Person B watches the results of Person A playing a game. There is no difference between Person B doing that and watching a movie. The game along with Person A are communicating information in the form of a story. Person A is also receiving the information.
*Edit* The more of your interaction is involved in the game would probably decrease the amount of information being received and make it less of a medium to you. IE, playing a sandbox game like Infamous, Prototype or Just Cause 2, where you're just putzing around town blowing shit up is not much of a medium, but while you're undertaking a mission, it is more of a medium.
See also; Choose your own adventure books.
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