Engagement means moving within a game which is not seen as such, since one is identified with it, lost within its parameters. The difference is more a matter of how than whether one continues to play the game. Mind is prominently a game player, a problem solver. Every form of mental activity that has a content, a structure, a goal, is a limiting game. This includes all forms of cognition and thought.
Every game generates a world .
A world is a game space, generated by a set of premises and rules, and projected as real. The world of Monopoly consists of every thing and action that is defined and allowable in the game. To the degree that human activities in the real world can be formalized, they are game-like. To the degree we intend an interpretation, the worlds generated by these games are the reality we actually inhabit. Machines as embodiments of formal systems are games.