You can try and define unique any way you want but there is no game term "unique rules", there is a game term "special rules" and they are defined and start on pg32. Unique was just a poor choice of words by GW, nothing more.
Not really, there is only one definition of Unique.
Oxford English Dictionary:
Definition of unique
being the only one of its kind; unlike anything else
The Axe Mortalis simply being master crafted does not make it unique, there are many other weapons that are master crafted.
Being called the Axe Mortalis does make it unique, no other weapons are called the Axe Mortalis, but simply being named is not a reason for a weapon to be listed as unusual, according to the rules.
Astorath's axe is unique, there are no other weapons in game terms that do what his axe does, making it one of a kind and unique.
Sorry, unique and the use of it are a bugbear of mine, it pisses me off when people say that something is "quite unique" or "that's really unique!" It either is or it isn't.