A few years ago I just decided that I was going to step away from discussions of what defines the game as an artistic medium. I was disillusioned because all the definitions I saw had, at their crux, the claim that a "game" is defined by either some element of challenge to be overcome by the player, or by the requirement that the player make choices.
These definitions always rang hollow with me. Many games I play have little or no challenge. Some games I play really require stretching the definition of "choice" in order to have them. Does it really make sense to call "when to press the buttons in rock band" a choice? Conversely, there's definitely no challenge in so many relaxation/simulation games, or freeform audiovisual playgrounds. I think all of these can fit together in one umbrella.
Okay, there it is. I like this definition. I've been working with it for about a year now.
It neatly covers why so many videogames are so compelling - they stick with you because you were doing the things. Mirror's Edge gets its kick because of how your control over the main character makes you feel like you're running and jumping across a city. Dragon Age is fun because, by making the decisions about who to do and what to say, you start to feel a strong identification with the character. The triumph at the end of a good Star Fox 64 run is entirely because I was the one who dodged the lasers and shot the enemies.
It also can be taken as an umbrella definition that encompasses both of the other definitions. If you define a game by a player's choices, well, those choices are necessarily a matter of player involvement. Similarly, you cannot challenge the player without granting the player some means to actively participate.
Furthermore, it meshes neatly together with one of the most fascinating things about video games as a medium in general: the consistent shittiness of their movie adaptations. Why do video game movies suck? It's simple: in the game, you fight against the ridiculous boss five or six incredibly frustrating times, and when you finally defeat them, you let out a whoop of delight and you're flooded with endorphins for your conquest. In the movie, you watch the protagonist get smacked a few times before defeating the boss. When the audience doesn't actually commit to the battle, and therefore doesn't feel the visceral frustration of actually failing, they do not care about the ridiculous situations video games contrive to put you in. Video game movies suck because the believability and power of video game stories always rely on the fact that the player has actually been doing something in the playing of the game - and that the player has changed as a result.
Since the medium's still pretty young, it's not commonplace to find examples of games that have neither challenge nor choice. What inspired me to write this post is one such game (at least, I'd claim it's a game): If the moon were only one pixel. I adore that page because it communicates the scale of space (this is very difficult to do), but also because it's a perfect example of my kind of game: There's no choice. You are not challenged in any way. And yet, the feeling of size and emptiness and vastness that it communicates cannot be replicated without the player actually scrolling through all that space.