Obaseki required his deputy to vacate his office after an acrimonious feud that ensued between them.

Like, I honestly do not get it. The office of the deputy governor is not an appointed position. Last time I checked, it is an elected position. Let's say you hired an accountant and discovered some faults in the manner he does his duties and had not decided to let him go yet. You could just ask him to vacate his office and move to somewhere else. Why? It is an appointment; a non-elective position. You get to decide if he stays or not. Same cannot be said of an elective position which the office of a deputy governor is.

Does a political office holder have the power to require another political office holder to vacate his office? Wouldn't that make Obaseki a very lawless governor? How is the deputy governor supposed to discharge his duties?

No matter the tale of benevolence by any political office holder to those he chooses to come up hither, he has no power to remove them. I don't under the democracy we practice in this country.