The controller asks him why he wants to come back to the airport. The pilot says due to an engine failure, then the controller asks if he's declaring an emergency, the pilot replies "no". The controller doesn't hear him so he asks again.
Well yes. just because some metal pieces might have damaged other parts/systems on the plane, like hydraulic, pressurization, or fuel lines. But essentially it's similar to an engine failure, since you only have 1 remaining engine in both cases.
I would call a Mayday on a separation.