Engagement is just verbal commitment between two families and no Ijaab-Qubool at all between the man and woman. Many times two are not even required to be present. They are still na-mehrum by strict sense.
What if in Engagment ,Both(Boy and Girl) are not Present and Ijaab-Qubool is made (Two Persons are Advocating i.e for the boy and the girle who are supposed to be engaged).
I think this time It is Nikah but known in Masses as Engagment as the Formality of Rukhsathy has not finished yet.