I don't believe playing game is fun only when we win. It is obvious that everyone likes to win. It has become a proverb that lose is bitter, or lose is orphan. I don't know anyone who plays to be a loser. On the other hand, every game has only one winner and one loser. Then why people like to play, despite they know, it is possible that they lose. The chance of lose or win is fifty percent. By the way, people accept these risks and even gamble. I think this question has several reasons.
First we play, not only for win or lose. We play games to enjoy and forget our problems. For example when I play backgammon, it does not important for me, who wins. Instead I try to enjoy, and I am happy, because I am spending my time with my family or my friends. If someone wants to remove games from our lives, I don't know what will happen, and what people replace it? do you know better entertainment?
Second, games are symbol of our lives. For example every day and every time we are in a real game that we name it life. I think games simulate our lives and we can learn a lot of things even we lose in games. It worth that, first we lose in virtual life instead of real life. If you have heard this famous quote of Napoleon Bonaparte that said, "I lost many times until I learned how to defeat", you will understand why lose always is not bad.
Eventually, in my opinion win is very tasty, but it is not disaster if we learn how to win. Therefore, it is essential winners teach us by defeat us. Maybe, that is why politicians like to play Chess. Maybe they want to taste lose in game and taste win in their life.