This leads to another question. What makes a game a fun game?
What is fun? It's a learned response (back to psychology). Playing games to win might be just one of an infinite number of possibilities, but I think we'll agree it's the most common.
Here's a rhetorical situation. Two boys play a board game for the very first time with adult supervision. The parents are all avid players and they have fun watching the game. The winner is cajoled and whether the game is random chance or not he thinks he did something right. The other player gets a pat on the back and a maybe next time, he's either bored or he'll cry for attention. Either way, one boy learns it's fun to win, the other boy observed it's fun to win.
Continuing on. In the case of the board game we have the fame vs shame phenomenon. Later in life the boys learn they are slightly talented in respective areas, one may know math with good hand-eye coordination, the other likes to experiment and is incredibly patient with attention in detail. If given a chance, they'll discover they win more when playing to their strength, they may even get better.
So this goes on.
Another more complex example. A high stakes player with the most money at the end wins. Just winning is fun. For a shark, new tricks earn even more money, and becoming a con artist through deception is very valuable.
Not exactly a change of topic, but the following will sound odd. It's possible for people to play games and sound like they are not having fun, specifically because it annoys them. I saw someone play games, not feel a challenge, and complain about how inevitable it is the game would force them to lose if they hadn't gone to extreme lengths to win. I can only guess they had fun in denial, or there was some extrinsic reward like adrenaline or masochism.