As the previous educator answer states, the amphitheater which the king builds in this story is personified as an "agent" which delivers justice. More than this, even the king's own "exuberant and barbaric fancy" is personified as something so powerful as to be almost separate from the king himself, capable of "asserting itself."
Later in the text, we can find other examples. The "doleful iron bells" which ring out in the arena, for example, are personified in that they themselves are not literally "doleful"—they are not capable of feeling this kind of emotion—but the writer ascribes that emotion to them, rather than to the person hearing their sound. The same applies later to the "gay brass bells" which elicit an opposite emotion in the listener.
Towards the end of the story, the human heart is also personified, imagined as something which can lead its possessor "through devious mazes of passion." In this example, the heart represents the whole person, making it an example of synecdoche also. Synecdoche is when one part of something is used to represent the whole thing.