The metaphor designates something (A) as something (B), something in the quality of something not itself.
It's necessary to deconstruct this sentence, but to aid that, let's reference a well-known metaphor such as sea of troubles1.
This metaphor designates a large number of troubles (A) as a sea (B), and one can imagine a shifting ocean, an amorphous mass of uncertainty, doubt and anxiety.
The highlighted portion of the sentence is rather stilted, but can be understood as
something: (A), "troubles" in this concrete example.
something not itself: (B), "sea" which is not actually troubles; it's actually water. "Something not itself" means "something else which is not A".
in the quality of: "having the likeness of," or "assuming the particular qualities of" or even "being rather like"
The metaphor provides a picture, a way of imagining something typically intangible as being like something else which typically is tangible. The qualities of the tangible thing are assigned to the original intangible thing.
Thus a sea of troubles.
The "something which is typically intangible" in my redefinition may be "something which is unimaginably large", and "tangible" could be thought of as "a graspable concept":
The metaphor provides a picture, a way of imagining something typically unimaginable as being like something else which can be more easily understood. The qualities of the mundane thing are assigned to the original unimaginable thing.
Shakespeare again: "All the world's a stage, and all the men and women merely players."
The world, which is huge, is reduced to the more comprehensible analogy of a stage, with people interacting as though they were actors.
"The metaphor designates the world as a stage, something not possessing the hugeness of the world."
1 Actually, that's part of a mixed metaphor, as Hamlet attempts to "take arms against a sea of troubles," and armaments aren't much use against a sea.