Why would I do this? When smarter people than I have already come up with more than +20 (here are just a few) definitions? Essentially, they don't work for me as a game designer-teacher-researcher-consultant. Up to now people have easily picked apart all the definitions I have used. Finally I am forced to define a game for myself... and here is what I came up with:
A game is a synthetic procedural system that stimulates regulated play.
A game is synthetic for two reasons 1) it is artificial or in other words 'not a real' procedural system 2) it also pertains to a synthesis of a procedural system.
A game is procedural, not rule based, because it reinforces ways of acting or progressing in a course of action. Procedural also indicates statements with conditions and consequences, while rules imply absolute statements.
A game is a system because it is a coordinated body of procedures.
A game can only stimulate play. After-all, it seems that +70% of games fail to stimulate any kind of meaningful play, yet they are still called games.
A game has various levels of regulated play (based on Roger Caillois's idea of game-play) because the play occurs around limited actions that players believe to be rules.