The king is semi-barbaric at the beginning of the story, and remains semi-barbaric at the end because he makes his daughter’s lover take the test in his arena.
The king is described as semi-barbaric because he is not very civilized. He thinks that justice is up to fate, and devises a cruel test involving a lady and a tiger between two doors, where the person on trial has to choose. The king considers this fair.
He does not change when he finds out about his daughter’s lover. He does not take revenge. He does not take pity. He has complete faith in his system.
No matter how the affair turned out, the youth would be disposed of, and the king would take an aesthetic pleasure in watching the course of events, which would determine whether or not the young man had done wrong in allowing himself to love the princess.
The king wins either way. If he chooses the tiger, he is dead and the king gets to watch him mauled. If he chooses the lady, he will be satisfied with her because she is pretty and he will have his life. As far as the king is concerned, everything is turning out perfectly. He has no moral issues with the process.