Although I'd like to add to that the caveat that "the way that events unfold" can be as simple as "the player character dies, or continues on"; I do count a simple "light gun"-style rail-shooter as a game.
 So many ninjas in games! [/edit]
Others have given definitions that I'd agree with, I think. To put my own definition in, I'd start by noting that "game" and "video game" are not necessarily synonyms, and that I'm going to define "video game", not
That said, I might define a "video game" as an interactive experience produced primarily via software, computer hardware or some combination or middle ground of the two. I suppose that the important part of that for this conversation is the term "interactive": a video game is in part defined by allowing the player some degree of control, whether over the order of events, which events occur, etc.
This can be very simple: imagine a game in which there is a completely static narrative spread out over an environment (perhaps via a mix of text-logs and events that can be triggered), and in which the player's only controls are determining the order in which they experience the elements of this narrative (by moving around and clicking, perhaps). To my mind this is a video game. Is it a good
one? That's another matter — and a very subjective one.
All of that said, I do think that one of the great strengths of games are in allowing the player agency (or at the least the illusion thereof). There are games that I think would be significantly weakened if translated to a more passive medium (such as film), simply by the loss of the player feeling that they
are the one making the choices. A good example, for me at least, is Planescape: Torment: the philosophy behind the game is, I feel, conveyed rather effectively in the player getting to choose the Nameless One's path, determine his nature and fate.
edited 20th Oct '13 3:41:27 PM by ArsThaumaturgis