What makes a videogame different than a game?
Let me try to answer this question using paradigms. Games, then, are the paradigm opposed to videogames. This paradigmatic opposition can be expressed in the form: [ videogames : games ]. The apparent difference between videogames and games is “video”. On the level of the medium that a game uses, this analogy is true, yet, peel away superficial visual component and the distinction begins to blur together.
A better name for what we usually call videogames would be “computer games” or “computed games”. More precisely: “games in which a computer fully automates the entire system in which you participate”, but this is somewhat flatulent as a name.
Saying that these games are videogames in the same way that Modern Warfare 3 is a videogame feels wrong. The former could be played without videos—simply as quiz games—whereas playing MW3 without a computer or console would transform the game into something which it is not.
A different analogy provides a better understanding: [ apparent rules : hidden rules ]. In traditional games, the rules are immediately and necessarily apparent to the players, since they must act as arbiters. In videogames, the rules may be hidden from the player, since the computer acts as arbiter; the player may simply play the game without reading the rules.
Thus, quiz games can never be videogames because in order to play them you must know the rules. In a videogame, however, there are no rules. By starting Minecraft and putting a character in a world, you are already playing the game, regardless of whether or not you decide to do anything thereafter.