If we go by technical definition of "emergency" then anything not by the plan is an emergency, but it's not used that way normally and it's not a technical publication.
If you are stuck in space with no lifeboat back then I agree it is an emergency, but they apparently have Starliner and it works. If they or Nasa are more comfortable with another option maybe that makes it an emergency or maybe not.
If it turns out Starliner doesn't work, that's an emergency. If there is radiation event coming then it's an emergency, but it is always an emergency in space regardless.
One, had. Starliner went home. Two, they didn’t. Starliner was broken. Its manoeuvring thrusters, a critical reëntry system, were misbehaving. If you’re on a plane and the oxygen system fails, that’s an emergency. You don’t have to wait for cabin pressure to fail for it to qualify, and oxygen systems aren’t even a critical system; this is closer to the flaps or landing gear behaving erratically.
If it fails then that's an emergency, but that regardless of the presence of the boat.
Noted the absence of Starliner, but not 100% convinced personally
It’s space. The ground state is emergency. I am training to be a pilot. Anything going off flight plan is an emergency. If ground control gives me corrective instructions, in the course of a mistake, I hope I will have the humility to not refuse its designation as a rescue.
Like, if you want an Exhibit A for why Boeing doesn’t deserve forward trust, it’s this response.