They were under no compulsion to kill the king since avenging Iphigenia's death was not--given the circumstances--a compelling reason to do so and their crime was, therefore, murder.
But their crime was also an assassination and Orestes, by virtue of his birth, believes himself compelled to avenge his father. The murder upset the political situation in Argos and Aegisthus's assumption of the throne was illegitimate and needed to be corrected in and of itself. Since Aegisthus and Clytemnestra were also tyrants the social order was doubly disrupted and allowing their crime to go unpunished meant acceding to this state of affairs. Failure to avenge Agamemnon, therefore, meant failing to defend justice in the political sphere. The 'world', therefore, demands this action. The actor is not free in the sense that if he wishes to be just he must act justly in ridding Argos of the tyrant. Since Orestes is also the only person who can legitimately take the throne from Aegisthus this is the only truly just choice that he can make.
Thus, in a moral sense, Orestes has no choice except between what is right and what is wrong when it comes to killing Aegisthus. The deeper quandary emerges in regard to the killing of his mother and it is for this reason that this act is the central concern of the Choephori. The play's title, which means the "libation bearers," focuses attention on the procession of Electra and the Chorus who offer libations at Agamemnon's tomb. Orestes asks later in the play "What prompted the Queen to send / This troop of mourners, with wine and oil / For her husband's grave" (117-18). He doubts that it is "remorse" that made her order it and sees it, instead, as "her latest exclamation / Of contempt" (118). Had his mother acted remorsefully--and had he been able to believe it--he seems to hint here that he could have been persuaded that her