Protagonist, by defintion, is the one character who the plot is centered upon. In this case, the young male villager serves as our protagonist because all of the story's action is oriented toward his eventual decision. We know he is the protagonist because of his portrayal as "the good guy" by the author.
The antagonist is primarily the semi-barbaric king, who makes the choice to have the young man choose in the arena either the tiger or the maiden. We have no way of knowing whether his alleged love (the princess) is an antagonist or not, as the author leaves us wondering whether the young man chose death or life. The princess gestures toward one door, but whether her love chose that door remains undisclosed. Further, we know that the princess was jealous of the woman behind door number two, which may have prompted her to lead her love to death rather than a lifetime with her adversary.
The protagonist of the story is the young man, a commoner, who is love with the princess. The antagonist is the king, who has thrown him in jail for secretly courting his daughter. He has decided to keep the young man away from his daughter for good by making him choose between the two doors, one with a tiger behind it or one with a beautiful maiden behind it.
Depending on the way the reader interprets the ending, the princess could also be the antagonist because she must choose which door to let her lover open. The story states the the princess has some of her father's barbaric nature. Because she has seen the maiden's beauty and becomes extremely jealous, she could very well have the young man open the door with the tiger behind it.