The young man, the courtier who is in love with the princess, is the protagonist. He is described as a typical hero. He is handsome and honorable, a "young man of that fineness of blood and lowness of station common to the conventional heroes of romance who love royal maidens." So, he is clearly the "good guy."
The first antagonist is the king. The king's version of justice lacks logic and seems to be more for entertainment purposes than for a genuine practice of justice. The king is "semi-barbaric" and it seems that the "semi-" description implies that one of the doors leads to the tiger and one leads to marriage. Thus, only part of his cruel game leads to death. The king's authority is "irresistible" and he was given to "self-communing." This means that he took no advice from anyone else. He ruled absolutely and according to his own whims. Prisoners sent to the arena were at the mercy of this barbaric king.
If we wanted to speculate further about the ending of the story, we could potentially say that the second antagonist is the princess. The author deliberately leaves the ending ambiguous, leaving the reader to guess as to whether the princess sent her lover to his death or sent him to marry another. Note that she is described as having a "soul as fervent and imperious" as the king's. This supposes that she might send her lover to the tiger's door because she may not be able to stand the thought of her lover being married to another woman.