Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third-Person (Omniscient)
The closest thing you'll find to a narrator comes in the form of the chants and songs that Churchill peppers throughout this play, because in these moments we have characters talking directly to the audience and revealing their true nature.
For example, at the beginning of the play we have Clive turn toward the audience and say, "I am a father to the natives here, / And father to my family so dear" (1.1.14-15). He's actually telling us the role he's going to play for the rest of play: that of the patriarchal dirtbag. One by one, the other characters in the play step up and introduce themselves and their roles.
In this sense, these characters are adopting the role of the narrator—because normally characters don't come out and actually say "Hey, I'm the patriarch" or "Hey, I'm the submissive wife"—but once they're done introducing themselves, the play just falls back into a standard dialogue-centric third-person omniscient script.