1) a player performs some sort of input into a game
2) the game responds with some sort of audiovisual phenomena in regards to that input
3) 1 and 2 are repeated, creating a relationship between the player and the game
I know a lot of people define video games as a series of choices or "states", but I think it's too strict as I don't think the appeal of video games is necessarily reduced to "a series of interesting decisions" as Will Wright puts it. I do think decision-making is a big part of a lot of games, but it doesn't explain the entertainment of situations like Revolver Ocelot torturing Snake in Metal Gear Solid, or groups of teenagers playing an easy Starcraft map against a computer player together. Animal Crossing is the same way too; the relationship the player has with the product is fulfilling, and that's what drives its appeal.