Being a process doesn't preclude something from being an entity. In particular, all of us living organisms have our constituent atoms constantly replaced, and we don't typically consider that a risk to our sense of self.
E.g. all "atoms" of a glider in Conway's Life get replaced every couple turns but an observer can tell it is still a glider because it keeps the shape, and it the same glider because it continues it's previous state.
This makes AI not quite alive because it's missing the continuity.
In a tortured semantics sense sure, but in a practical sense they refer to different types of things.