Symbolism, Imagery, Allegory
In Cloud 9, being a father is a symbolic role. It means more than being a dude and having a couple of kids; it means having everyone obey you at all times. From the play's opening lines, Clive establishes himself as not only the father of his family, but as the symbolic father of everyone around him, claiming, "I am a father to the natives here, / And father to my family so dear" (1.1.14-15). If you're looking for an appropriate adjective to describe this kind of mindset, the word is paternalistic: Clive believes the father is a figure who automatically rules over other people.
And as you can also tell from Clive's opening speech, he considers himself not only a father to his family, but a symbolic father to all of the black African people living in the villages around him. Through Clive, Caryl Churchill shows us how closely the racist legacy of colonialism is connected to the history of gender inequality. Clive even makes this connection himself later in Act 1, when he tells his son Edward, "Through our father we love our Queen and our God, Edward. Do you understand? It's something men understand" (1.3.123-125).
Clive basically believes that the right to have control over other people all comes back to being a strong white man. Clive doesn't demand respect and obedience because of what kind of person he is. He simply expects it because he's a man—a symbolic father—and his views on this sort of thing never really change in the play, even though the plot of Cloud 9 endlessly undermines Clive.
If there is a main moral to this play it's "Don't be like Clive."