An example of foreshadowing in the story could be the fact that the reader knows that the Princess hates the beautiful young lady who waits behind one of the doors. She is extremely jealous of her, and it is logical to conclude that she will not signal her lover to pick the door where the lady waits to marry her beloved.
Its safe to infer from the facts of the story that the young commoner picked the door with the ferocious tiger.
I think that the fact that the Princess can't have her lover is evidence enough, along with her jealous hatred of the beautiful young lady, that the poor commoner gets attacked by the tiger when he opens the door that the Princess directs him to choose.
The irony, I think lies in the King's use of the arena as a system of justice. The fact that the day of the commoner's trial is suggested to be an orderly process that is somehow fair is ironic. The outcome is being determined by the Princess's hatred and jealousy of the beautiful young lady. There is no doubt that the young man is killed by the tiger.
Justice is an orderly process where the accused is entitled to a trial to determine guilt or innocence. In the King's justice, the use of the word justice is ironic, it is not justice at all, but pure entertainment for the King and his subjects.
The only judicious purpose that the arena serves is to discourage the King's subjects from breaking the law. Public executions are a good deterrent, they discourage crime very efficiently.