A Model of Play is a fascinating poster (available as a PDF or as images) that takes what seems like a very game-grammar point of view on the concept of play — even freeform play.
In play, one of the primary goals is to have fun — to continue engaging in the conversation that creates fun. Individuals choose the means for achieving that goal; they choose the topic of conversation, for example, which game to play. Within a topic, they choose different strategies and pursue a series of sub-goals, adjusting means according to their effectiveness. Goals and sub-goals and associated means form a tree (or web) of possibilities for action.
Among the grammar principles that are mentioned is the notion that play always requires two, even if the second person is a “virtual person.” The notion that interactivity is inherently a conversation can be traced back to at least Chris Crawford, of course.
Also cool is the “step by step” logic version found here, which builds the poster argument by argument.