Many luminaries have defined the word "game", from philosophers such as Wittgenstein to game designers such as Chris Crawford.
One thing you learn from all of these definitions is that the definer deliberately decides before giving the definition as to what games will be included in the definition and what will not be. In all of the definitions, the definer leaves out some things called "game" that others would include.
For instance, Chris Crawford defines an activity without the ability to interfere with your opponent as "competition", while one with the potential for interference a "game". Surely he would admit that many other people think of the 100 meter dash as a game. Chris is not really interested in what the definition of a game is. He is more interested in using his definition to make points about player interaction and what makes a good game.
Raph Koster's definition of game includes such concepts like learning and fun. Because he wants to talk about learning and fun.
Another says that a game must be childlike and not taken seriously. If you present this person with a non-childlike game, he will either try to explain how it is, in fact, childlike, or instead claim that it is not, in fact, a game.
Childlike? There are plenty of games that are not for children.
Fun? If you're competing to win $10,000,000, you may find it no fun at all to play.
Interactive? Chris may tell you that racing is not a game, but many others would disagree.
Has rules? There are games that don't have defined or circumscribed rules, not to mention games where the rules change as you play.
Has a winner and loser? There are lots of games in which everyone can win or lose.
Abstracted from reality? What do you do with people who turn their everyday tasks into a game? They're doing activities which are not abstracted in any way and they win or lose concretely at the end. What about people who claim that life, itself, is a game? It's easy to wave your hand and dismiss this as metaphorical, but if it's not meant metaphorically? Can you so easily insist that life is not a game just because it doesn't fit your definition of what a game should be?
The word "game" thus seems to have a tenuous grasp on any sort of definition. Like art, if we define everything as a game, then nothing is a game. So it behooves us to find at least something that we can pin down to say that it, and nothing that is not it, is a game, or at least may be a game. Luckily, unlike art, there are a few things that we can definitively say about games.
1) A game is an occurence. Something happens. The game is what happens. If the world starts in state A, a game cannot have existed until the world is in state B. Games occur.
Consider the following game: two people watch a leaf fall. One says that the leaf will land pointing left, the other that it will land pointing right. A game is being played. The leaf falls.
A game need not be completed for it to have been called a game. Suppose the leaf is blown away before it falls, or the two players abandon the game midway. A game has still occurred.
Of course, many people use the word "game" when referring to the components of a game. For instance, they will say that this box of Monopoly is a game, when it is, in fact, the components that are used to play a game of Monopoly. That's fine; the components of a game can be filed under the word "game" as a separate entry in the dictionary.
2) A game rests as an abstraction over reality as it occurs.
Suppose you turn your job into a game. You tell yourself: I'm going to file all of these documents by the end of the day. If I succeed I win, if I don't I lose. The plan is to file the documents by the end of the day; the game is the reward of "winning" or "losing". The plan is concrete. The game is abstract.
You do the same concrete tasks and achieve the same concrete results. Only now there is a layer of abstraction on top of this: "I win" or "I lose". You could just as easily have said the opposite: I win if I don't get all of this filed, I lose otherwise. The declaration doesn't change the concrete nature of your work, only your attitude toward it.
This element of the game, which is an award for completing the game in the form of acknowledgment or shame, was added to the concrete task but has no specific reality other than within the game's world.
The promise of a reward may concretely affect your behavior, but this is because you like to play games. The game is a motivating force. The presence of the abstract affects the concrete, just as thoughts about a vacation or a lover can affect your performance.
3) A game must involve the conceptualization of multiple events.
A person need not know he is in a game to be playing one. Nor do games require decisions, teams, interaction, a possibility of success or failure, skill, or luck, per se. However, regardless of whether the future is pre-ordained, there must exist a conceptualization of an alternate future.
For instance, I may play the following game: If the sun rises, I will be happy. I wait for the sun to rise, and then it rises. I have played a game. The concept of the sun not rising exists, even if there is no possibility that it would not occur.
Note that if I say "I will be happy when the sun rises" I am not playing a game, whereas if I say "I will be happy if the sun rises" I am, or may be, playing a game.
In other words, whether cognizant of the game in which you play or not, whether for only a brief moment or more, a game can only be a game if somehow the future can be measured by more than one possible outcome.
With these three elements, we can say that anything that is not "an occurence which is abstracted over reality and permits the idea of multiple futures (or permitted, if the game is already finished)" is not a game.
A fourth criteria could be: there are different motivations for wanting each possible future. But this might imply that the future is within reach. Imagine a game that takes eons to play, each person playing, or rooting for, a small part, with no knowledge of how his or her part will turn out. Motivations are there, but not the rewards.
For the broadest definition of the word game, the three elements are all that you need. Man, beast, or machine looks to the future with an idea of what may happen but without perfect knowledge, and abstracts the future into possibilities which overlay reality: that is a game.