MDA, if only we could work another M in.

What a 'Game' is is the subject of some debate, or at least was until Robin Hunicke, Marc LeBlanc, and Robert Zubek advanced the conversation (http://www.cs.northwestern.edu/~hunicke/MDA.pdf). Currently, the working model of 'Game-ness' involves three factors: Mechanics, Dynamics, and Aesthetics.

Mechanics are the particular rules and procedures of a Game, or as I have begun to think of it: Mechanics are the walls defining a boundary. Phenomenologically, a Player Entity entering this Mechanical space instantiates a Game. The Dynamics are movements (actions and choices) of the Player within that space - their limitations being dictated by the Mechanics. The Mechanics are what a Player can do, the Dynamics what they do (and to a lesser degree, but none the less utilizable, what they don't) do, the Aesthetics (a relationship between the Mechanics and Dynamics) are the methods which the Game uses to engage the Player. More generally, Aesthetics are how the Player feels: why they do what they do.

There are nine main ways Aesthetic manifests:

• Sensory - This could be a Game having a distinct visual style, or a particular emphasis on sound, or even the way the controller is used and the buttons are pressed. A Game could be pleasing to the taste, smell, or ability to see dead people, but I personally can't think of any examples.
• Fantasy - The Game employs a particular perspective, allowing the player to experience a role or ability, and while that might be something fantastical, it need not necessarily be. A simulation of something tedious would still most likely fall into this category.
• Narrative - The Game engages through a rich story, and Players 
• Challenge - The Game exists as an obstacle to be overcome. While many Games may use difficulty (in the strictest sense) in this manner, the similar effect could be achieved with requiring a Player to not only prevail, but with style or grace.
• Fellowship - Players cooperate with other Players to accomplish tasks that might be too daunting or unable to be completed by a single person.
• Competition - The Game pits Players against other Players, changing the primary antagonists from Game AI to real-world entities with Human intelligence. 
• Discovery - Players unlock and uncover aspects of the Game, whether it be exploring levels or developing abilities or seeing new cards. The Player begins with little or no information, and must build up from square one.
• Expression - Games utilizing Expression often provide the Player with blank slates on which they can project aspects of themselves. This could be a design-a-character feature where a Player designs in-game objects, or even branching fiction, where the Player chooses possible Narrative options.
• Abnegation - The Game is a enjoyable recreational activity. This seems especially subjective.