You’re talking about simple conquest. By that definition any offensive side in a war is imperialist, which is nonsensical as that means nearly every war in human history involved at least one “imperialist” power.

Imperialism is system of establishing and maintaining hegemony over large areas for the benefit of an elite (capital in modern times, patricians in ancient times, etc) within a metropole (probably too simple of a definition but it works). The Romans were an empire not just because they had an emperor and not because they conquered lands, but because they controlled lands from Spain to Syria and wealth flowed from those lands into Rome.