The commentary notes that some logicians subsume the eight identities under identity of subject and predicate. On that analysis, time, place, condition or relational object is already contained in a fully specified subject or predicate.
In “Zayd is in the house now” and “Zayd is not in the house now”, the fully specified predicate being in the house now already includes time and place.
This does not make time or location irrelevant. Both approaches demand an affirmation and denial of one precisely determined relation. The difference is how its qualifications are organized.