If we look at the example, the lack of contradiction is one condition, but there is another one - totality.
The sentence "the whole sphere of possible existences, the mortal occupies one part, and the immortal the other." contains the assumption that all objects in the universe are either mortal or immortal, which is questionable e.g. what about the things that are not alive in the first place? e.g. is a chair mortal or immortal?
This issue is not present in the dichotomy between reality and negation e.g. the dichotomy between "mortal" and "not mortal" - here it is easy to sort all possible objects to mortal, e.g. a chair is clearly not mortal. In my view this is the difference between reality and negation.
Happy to read your thoughts on the subject.