@Deckard,
What about games in which there are only one participant?
Historically, there have been many different "rules" in war. For example, at one time if a fortress surrendered before the walls had been breached, the inhabitants could not be put to the sword. Later, the time a battle would begin and end for the day would be arranged by the leaders in advance. Recently, treaties specify the treatment of prisoners and forbid certain practices in battle.
Didn't Wittgenstein remark that "game" was really a series of family resemblances---that there was no single characteristic that ran through all the different games to unite them, but rather aspects of some games that bled over to others that, in turn, would have some that were shared with entirely different games.