I vacillate when it comes to defining words. Not on the word's definition, but on the need to define them.
For example, there is a big and continuing debate as to the meaning of several words I use regularly, such as 'game', 'meme', 'play', 'think', and 'stupid'. Sometimes, I look at the word and say, "The exact definition doesn't MATTER. Communication is all that matters!"
Other days, like today, I think "the word doesn't help us to communicate unless we define it. Furthermore, DEFINING the word is, in itself, valuable communication."
My favorite definition of 'game' used to be Crawford's definition, which talks about the difference between a toy, a puzzle, and a game. But it never sat quite right with me. So I made my own, but I'll get to that.
Today, Darius and Bill were chatting about a group of fairly uninteresting academic "games" which are, in truth, just puzzles. Darius is of the opinion that they are games because his definition of game is extremely broad. Bill seems to agree with him now that it's been said. I don't.
Why is it important? Who CARES what a game is, after all? Whether you're making games, toys, puzzles, or 'interactive entertainment', who cares?
Well, that's just it. There's a big difference between a puzzle, a toy, and a game. The types of enjoyment you'll have are distinctly different in each. To be blunt, each is a different kind of 'fun' and sells to dramatically different audiences.
I won't say that any one is superior - I love all three - but they are TOTALLY DIFFERENT PHENOMINA. Think about it. A puzzle is something you mull over, plan out, try a few things, start over because they don't work, and eventually 'solve'. A toy is something you play around with, manipulate, and push into interesting new configurations. One is goal-oriented, sure, and the other isn't... but it goes deeper than that.
A puzzle is a 'one-shot'. It's a single encounter with no ramifications or meaningful results. You either solve it or you don't. A toy is a continuing affair. Most of the actions you take have results, which you can then deal with. Moreover, 'toy' does not imply 'challenge'. Barbies are toys, but there is no challenge there. You just play.
The key difference is: the first has no feedback loop. The second does.
Once you've 'solved' a puzzle, it's probably done. Unless it's extremely complex (complex enough to be very difficult to memorize), you solve it once and it's dead for you. On the other hand, something with a feedback loop can be played in many different ways. You can return to it again and again. Barbie went out with Ken last time, but this time she's going out with Brittany. Or the Predator. Endless permutations are available.
I say that a feedback loop is a CRITICAL part of games. Look around. Everything you consider a game has a feedback loop. You do something, and it feeds back into the game such that your next action is influenced by it. THAT is what makes a game fun. To say that 'puzzles should be considered games' is to lump apples and tequila in the same group. Yes, they're both comestable. No, they're not the same, and they have wholly different audiences. And the audiences know it.
I would define a game as a series of feedback loops which allow player input and follow rigid rules. A toy has no rules. Although Barbie herself has rules - she can only move in specific ways, she weighs a specific amount, she has no nipples - PLAYING with Barbie has no rules. A game is the same, except that it has very definite rules. For example: throw Barbie through the flaming ring across the lawn, best out of five.
(BTW, the feedback loop there is simply that you can take into account your earlier throws with each throw - 'learn' to throw better.)
So, that's my definition of 'game': player-affected, rule-based feedback loop(s). Your game may also have toy components, such as telling a story in the Sims, but at the core, there is a rule-driven feedback loop which you have to deal with.
And it's important, because you're selling to an audience. The audience knows the difference between games, puzzles, and toys.
I'll give you a hint: puzzles don't sell very well in comparison to games, but toys do. That implies that the feedback loop - the freedom and power of experimentation - is the important part.