I have to agree. The whole concept doesn't make sense. How do you define a game, especially when it has no players? 

The first sentence defines a zero player game as a game without any human players (no citation). The second sentence defines it as a game played by artificial intelligence. Whether the player is human or machine, there's still at least one player. 

And if the Game of Life has no players, is it really a game? Or is it an algorithm or mathematical "thing"? If you grow a flower or a crystal, its not a game. So when you grow the "Game of Life", is it really a game? 

Or if one considers the programmer/user as the player, since they will be the one to pick initial board, then it's not really a zero player game.