The "triple-gorged spirit" or "Fiend," depending on the translation referred to, appears to be some mythological divine figure that haunts Agamemnon and his family, resulting in the deaths that have occurred in the play and before. Clytemnestra sees herself as an agent of this force, but the Chorus only bemoans there helplessness in the face of the gods, and in particular Zeus, who clearly planned and preordained the death of Agamemnon. Note what they say:
Truly you speak of a mighty Fiend, haunting the house, and heavy in his wrath (alas, alas!)—an evil tale of catastrophic fate insatiate; woe, woe, done by will of Zeus, author of all, worker of all! For what is brought to pass for mortal men save by will of Zeus? What herein is not wrought of god?
Even though the murder of Agamemnon by Clytemnestra is described as "an evil tale of catastrophic fate insatiate," it is clear that the Chorus believes that Zeus, as the ruler of the gods, must have planned this to happen. Note how he is referred to as "author of all, worker of all." Even though Clytemnestra was the human agent of the death of Agamemnon, Zeus must have planned this to happen, the Chorus argues, and therefore is ultimately responsible for Agamemnon's death. The two rhetorical questions at the end of this quote serve to underline the point that the Chorus is making: if Zeus did not will Agamemnon's death to happen, it wouldn't have occurred.