Setting the ground work for what makes a great game

At an abstract level a game is merely a situation that involves actors that have a set of rules imposed on them. Generally the rules apply across the board to the actor(s). Games also usually present some sort of objective or state in which a particular actor may win either against the game as an abstract entity or against other actors. In following the objectives of the game and adhering to the rules an element of challenge is presented to the actor and thus makes the game fun. The level of challenge is a delicate one however because something too simple or too difficult can quickly lose that element of fun for any given actor.
To keep this short and maybe even make a point, what really makes a great game is an ideal balance of challenge. This ideal amount presents the actor with a challenge that tests their skill but isn't immediately impossible for them to accomplish. Many games use an iterative cycle of increasingly difficult challenges, also known as levels to allow actors to rise to their own level of competence within the game. Once there, the actor much put a good deal of effort into what ever skill they may rely upon in the game to advance further.