Note: This is (probably) the only article where I will actually distinguish the term "game" from "videogame". Every other place will use these as synonyms, except when we are actually discussing the game-like character. In those cases, I will use specific language to distinguish them. Unless the context suggests otherwise, you can assume that the term "game" means "videogame".
More and more, we hear about things called "non-games." Things like The Sims, Second Life, Brain Age, etc. There are basically two definitions of non-games: videogames for people who aren't traditional gamers and videogames that aren't games. So, let's discuss what it is we're talking about.
First, let's define the term videogame. A videogame is an piece of software or hardware whose primary designed purpose is to elicit some form of enjoyment or entertainment. This separates videogame software from, say, Word or Photoshop. Plenty of artists have fun with Photoshop, but it's primary designed purpose is to empower the user with regard to editing images.
Now the phrase "primary designed purpose" is key. Why? Because Mario Paint is a videogame while Photoshop isn't. And this is not simply because Mario Paint came out on a console and Photoshop didn't. Eletroplankton is a videogame, despite the fact that it could be considered a strange combination of Photoshop and a sound synthesizer.
The reason Mario Paint is a game is because its user interface for editing images is designed for the purpose of making it fun, not useful. You can do things of value in Mario Paint, but the main purpose is to fool around, stamp out some nifty animation with Mario characters, and so forth. Maybe if you really get into it, you might try something serious, but its tools are really too simplified for that.
Microsoft Paint also has simplified tools. The primary difference there is that Paint's simplification is not designed so much for entertainment, but for ease of implementation. For just about every one of Paint's features, there is an equivalent Windows graphics API call. In short, Paint is really a thin user interface over the Windows graphics API.
Photoshop is designed to give the user powerful features for editing an image. This is its primary purpose. Whatever enjoyment comes out of using Photoshop is provided by the user's enjoyment of creating art, not the designed intent of the Photoshop developers. They merely provide what is useful towards the end of creating images.
So, a videogame is merely an electronic "device", hardware as in the earliest days of arcades, or software as in modern times, that is designed for the purpose of being entertaining.
However, that doesn't deal with the Game vs. Non-Game distinction.
Personally, the distinction between the two comes down to the traditional definition of the term "game".
What is a game? Well, a game is a set of rules for interacting with something and a set of objective conditions that determine when the game ends and who won, if anyone. This definition covers everything from Chess to Tic-Tac-Toe to Super Mario Bros. So, what doesn't it cover?
The Sims, for starters. SimCity as well. Will Wright famously and rightly states that these are not games; they're toys. A toy is something that has a set of rules for interacting. You can bounce a ball off of objects, but you cannot turn it inside out (well, you can, but it is a different object now) That is, a game is a toy that has explicit victory conditions.
Brain Age is a game. It is a game because it has an explicit score, and you know when you've won, because it tells you. Old-school arcade games that measure success by score are games. Competitive FPS's are games.
Note that the definitions of "game" and "videogame" are not related at all. There were games before videogames, and there are videogames that are not games. I use the term "videogame" as opposed to something that doesn't use the root word "game" simply because it's more widely know. I could say, "Interactive Entertainment" or something of that nature, but it's difficult to know how that is different from table-top Chess.
So what is the difference between a game videogame and a non-game videogame? Gaming videogames are about one thing: winning. The Interactive Loop is used to improve the player's skills and provide appropriate challenge. Mechanisms of design create interesting Situations for the player to overcome. And the design gives the player a way to tell how well they're doing and whether they "win". But even victory is secondary to the enjoyment gained from the Situation-to-Situation momentum of playing the game.
Non-gaming videogames use the Interactive Loop for some other purpose. Simulation-type videogames use the loop for the purpose of modeling a simulation, whether based on real principles or not. What matters in those videogames is how interesting the simulation is and that the rules of the simulation create interesting situations. These too have a degree of Pacing, though in their case, it is not always based on challenge; it depends on what the player chooses to try to achieve with the simulation. The quality of a simulation videogame is judged based on how interesting the situations that it naturally creates are, and how these situations flow one into the next, much like for gaming videogames.
There is a great deal of potential for finding other uses for the Interactive Loop. For example, Electroplankton uses the loop, not specifically to create a simulation, but to create audiovisual patterns. There is no victory; it is simply about the player creating an interesting audiovisual effect. Mario Paint does something similar, though in a more traditional way. Some videogames have even tried to deliver narrative content through the Interactive Loop, though with limited success.
Note that these are not hard-and-fast categories. Simulation-type videogames can have substantial elements of gaming properties, and vice versa. We will deal with this later as we look more in-depth at game design.
As for videogames for non-traditional gamers, the distinction matters, but not from a design point of view. Granted, videogames of this type tend to have slower pacing models and generally less complexity in terms of challenge and/or fewer dimensions of challenge. Their purpose tends to be introductory in nature, which is a reasonable goal.