Often in the translation, god(s) is simplified to god or even God. You are right in that the Greeks were not only polytheists, but this referral to "God" likely isn't the same God we recognize most in Western culture.
At the beginning of the play, Oedipus sends Creon to speak to the Oracle at Delphi. This means he was seeking wisdom from the god Apollo. Historically, medicine and healing were both associated with Apollo. Likewise, was looked at as one who could inflict ill health and plague. Oedipus appeals to Apollo because the city of Thebes is suffering from a pestilence and plague. Very likely then, unless otherwise specified, the rest of the referrals to "God" throughout the play are also referring to Apollo.
First, the Ancient Greeks weren't necessarily polyatheists. They are better classified as polytheists with some elements of pantheism. Keeping that in mind, the origin of Greek theatre plays a significant role in the traditional elements found in Greek plays. The Greeks originally created theatre to pay tribute to Dionysus--a Greek god. Thus, Greek playwrights, whether they personally believed in a Supreme Being(s) or not, would have been obligated to include references to god(s) in order for their plays to fit the theatre's festival spirit and traditions.
Similarly, the Ancient Greek playwrights/bards portray god as a moral/cultural code by which the Greeks were supposed to live rather than depicting a specific higher power figure. In Sophocles' Antigone, the chorus and Choragos serve as reminders to Creon of what he should do; they are a conscience of sorts. Likewise, the oracle and prophet Tiresias often deliver messages to characters, messagethat contain omniscient elements or moral guidance from a godlike power. This concept from Greek drama not only enables the playwright to pass down Greek traditions, but it also promotes a type of absolute morality, which Aristotle later focused on in his discussion of ethics.