I think this story has a lot to say about the importance of choice and the consequences that result from that choice. Consider the "beauty" of the arena that the king has created: the prisoner's choice is the one that will decide his destiny, not the king's choice for him. He will either perish by getting killed and eaten by a ferocious tiger, or he will instantly marry an enchanting maiden. This "choice" that the condemned person must make absolves the king from any kind of responsibility and simultaneously makes judgement an entertainment form as the crowds want to see the action and outcome, full of suspense to see what will occur.
Of course, the young man is not the only person with a tough choice to make. The princess, his lover, likewise needs to make a choice between life and death - but it is a choice not for herself but for him. However, either choice means "death" for her hopes of love and marriage. The author presents the princess as wrestling with both options and the outcome of each in great detail, and we are left with crucial ambiguity about how she will decide, leaving generations of readers to try to guess her choice and its consequences:
The question of her decision is one not to be lightly considered, and it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you: Which came out of the opened door - the lady, or the tiger?
Note how the author puts us in the position of the crowd, eager to see how the prisoner will choose and the consequences that will befall him.
In my opinion, I think the characters are all unimportant to the message developed by the short story. This can be seen when how the characters are developed are examined. They are all sketched in very quickly by building on conventions, and their descriptions rely on hyperbole and absolutes. Ones such as, "As is usual in such cases, she was the apple of his eye, and was loved by him above all humanity. Among his courtiers was a young man of that fineness of blood and lowness of station common to the conventional heroes of romance who love royal maidens." Note that the narrator draws on many conventions and makes many assumptions; this has the effect of quickly sketching them in just so that they could serve a plot function. Something else to consider is the setting. It is similarly quickly sketched in and is similarly described using hyperboles and absolutes. This can be seen when the narrator describes the tiger as the cruelest and the maiden as the fairest. The question comes then, what is the most important part of this short story? This is bluntly explained by the narrator right after the climax, where it is revealed that the point of the story is whether the tiger came out or the lady. However, I do not think that is the question the audience should and would dwell on. Rather, it is whether had they been put in the position of the princess, would they motion to the tiger or the lady. This story presents a dilemma, where one has to choice between two equally undesirable choices. These two choices ultimately reflect on two key human emotions; despair and jealousy. The message in my opinion, to the audience is a question of human nature; whether despair or jealousy dominates one's mind. This would be how I would describe one of, if not the most important, messages presented in this short story.
Sources would include ELA 10, thank you Miss Groen.