It's just a Spirit.
As you determine the characteristics of it, in layer 4, there's two effects, one from Olivia (becomes a Vampire) and one from Haunted Plate Mail (becomes a Creature and a Spirit in addition to previous types and subtypes). Since there is no dependency the two effects, you apply them in the order they were created. First, you try to make it a vampire - which doesn't do anything because it's neither a Creature nor a Tribal, then it becomes a Creature - Spirit.
As for the explanation for the lack of dependency, see my previous answer about Gideon Jura and Olivia:
The whole question is then to know if there is dependency between “becoming a creature” and “becoming a vampire.” Even though the result of “becoming a vampire” is different whether you apply the “become a creature” effect or not, what matters in order to have dependency is if what the effect _attempts to do_ is different. Here, what the effect attempts to do is setting the object's subtype to vampire, and this doesn't depend on whether the object is a creature or not.
Daniel Kitachewsky
L3, Paris, France
Rules NetRep