The dictator game is barely a game at all. It is used as a study of
game theory which illustrates that simplistic application of
self-interested models of
choice are incomplete.
In the dictator game, there are two players. One player is the "Dictator", and the other is the "Receiver". The Dictator is given some amount of money (say $20 in $1 bills). The Dictator gets to decide how much of that money they will keep, and how much to pass on to the Receiver. The Receiver doesn't get to make any choices at all. They just take what they are given, thereby the "Dictator" name.
Assuming people are completely self-interested, the prediction is obvious--the Dictator should keep all the money. In fact, Dictators in experiments typically pass along some of the money.
Like the ultimatum game and the investment game, the dictator game is used to study alternatives to self-interest in economic models.