It is addressed to the people: this was answered by the Congregation of Rites in 1816.
There are 3 ways the Mass can end:
Ite Missa Est
Benedicamus Domino (Let us bless the Lord-before 1960, used for various Masses particularly those of the Lenten feriae)
Requiescant in pace (May they rest in peace- for Masses of the Dead)
Prior to 1960, the priest would recite things said/sung by the other ministers, hence a question was posed to the Congregation:
An sacerdos dicere debeat in missa solemni, Ite Missa Est, Benedicamus Domino, et Requiescant in pace, vel dicantur tantum a diacono?
i.e. should the priest also say the words or should they only be sung by the deacon. To which was replied (September 7, 1816)
*
Quoad Ite Missa Est, negative, quoad Benedicamus Domino et Requiescant in pace, affirmative*
the interpretation given being that the latter two “had the character of a prayer” while the former did not.