What is similar about the presentation of the scene of the execution in the image and the text is that both demonstrate that Dionysius is in command of the situation.
In Damon and Pythias, Pythias is condemned to death by Dionysius, a Greek politician who ruled Syracuse. In the myth, Pythias asks permission from the ruler to return home and set his affairs in order, which implies that Dionysius has the power to decide everything. Moreover, it is the politician who also determines to free both Damon and Pythias. Therefore, throughout the story, it is Dionysius who controls the fate of the two friends. This can also be seen in the image, where Dionysius is sitting on the throne wearing his crown. Furthermore, the ruler is pointing someone, which indicates he is giving an order. He also has his army standing in front of him and a soldier behind him for protection.