The qualities that set Murder in the Cathedral apart from a typical realist drama of the 1930s are its use of a Greek chorus and its Medieval miracle play motif.
Murder in the Cathedral is a didactic drama teaching its audience the importance of integrity in a Christian context. It was commissioned by the Bishop of Chichester, George Bell, as a response to Adolph Hitler's 1934 Night of the Long Knives, in which the dictator had many of his associates murdered without a trial.
In Greek drama, a chorus comments on the main drama. The humble women of Canterbury constitute the Greek chorus for this play, providing normative commentary on the decisions and actions of the main character(s)—in this case the archbishop of Canterbury, Thomas of Beckett.
The play also follows some of the conventions of the Medieval miracle play, as it is, like a miracle play, about the life of a saint. The play is heavily theological, with Beckett having to face not three (as Christ did), but four temptations to do the wrong thing. He knows he must allow himself to be murdered rather than go along with Henry II's wrongdoing. However, his desire for bodily comfort and prestige tempts him to capitulate, as does the temptation to stay alive by rationalizing he could do good in his position as archbishop. A third temptation is to lead an overthrow of the king that would give the church more power, and a fourth is the temptation to die for the glory of being a martyr rather than because it is the right thing to do.
The play has a static quality, as it is focused on Thomas's spiritual struggles with commentary from a chorus.
It should be noted that there was much experimental drama being written at the time. Eliot's drama differs from conventional theater but is hardly unique in pushing conventional boundaries. His intent was to provoke audiences to think about the importance of standing up for what is morally right in the face of evil.