Emergency, at least in FAA parlance, means that a plane is given special services like priority access to airspace or a runway, typically, but not always, at the specific declaration of "emergency" by the crew to handle an in-flight situation.
In your case, the crew used back-up systems to complete the flight and, since there were probably no other planes around, had no need to declare an emergency to get access to the runway immediately. No need to increase the paperwork further by invoking the "E" word.
Thanks for the explanation!