According to "The Lady or the Tiger," "No matter how the affair turned out, the youth would be disposed of." What does this mean? Would justice have been administered fairly?

In Frank Stockton's short story "The Lady or the Tiger," the young lover of the king's daughter is accused of a crime and judged in the king's arena. The man's crime was simply that he dared to be the princess's lover. His appearance in the arena is the king's way of getting rid of the youth because the king believes the man is not good enough to be with the princess. He is a commoner; the princess, royalty. For the king, the arena is the perfect vehicle to dispose of the youth because, after choosing one of the doors, he will either be consumed by the tiger, or promptly married to the lady, "the most suitable to his years and station that his majesty could select among his fair subjects." Regardless of the outcome of the "trial," the princess will no longer be able to see the young man and their love affair will be over.
For the "semi-barbaric" king's way of thinking, the outcome will be perfectly just. The accused's life is in his own hands. Unfortunately, the king's "incorruptible" justice has been corrupted when the princess discovers the secret of the doors and motions to her lover as to which door to choose. It is left in question whether the princess directed him to the lady or the tiger. If she had somehow quenched her passions, she may have chosen the lady, but, if her "semi-barbaric" nature got the best of her, then the young man was certainly doomed. In practical terms, because the young man was only guilty of loving above his status, the only just outcome would be if the lady emerged from behind the door. If he is eaten by the tiger, then the princess should be described as "barbaric," not "semi-barbaric."