In Stockton's short story "The Lady or the Tiger?" the people of the kingdom came to watch the accused fate be played out on the grounds of the arena. The arena was constructed
not to give the people an opportunity of hearing the rhapsodies of dying gladiators, nor to enable them to view the inevitable conclusion of a conflict between religious opinions and hungry jaws, but for purposes far better adapted to widen and develop the mental energies of the people.
That being said, one can only assume why the people came. The thoughts of the king are irrelevant.
Historically, people came to trials such as the one detailed in the story, as a form of entertainment. Not only were trials held in the classical arena, challenges were faced, life was given and taken away in battles of egos, and games were celebrated.
Therefore, the people of the kingdom most likely came because it was a place where they could be entertained, meet up with others (a social gathering), and see the consequences of improper behavior as defined by the king.
One could only assume, since readers are not explicitly told, that the people came of their own free will. While one can be sure that propaganda was laid out about upcoming events in the arena, one can also be sure that the people were also just as semi-barbaric as their rulers and wanted to see blood.