Just some terminology before the actual question so you understand what "predicate nominative" really means.
Subject: Discussing the one who does something or is something in the sentence.
Predicate: Discussing the action which the subject does in the sentence.
In this sentence:
Subject: Chess
Predicate: has always been one of Henry's favorite board games.
Nominative: Describing the subject (words following to be, to seem, etc.)
Accusative: Taking a direct object (such as to have, to see, to tell, etc.)
Dative: Taking an indirect object (such as to go to, to look at, to say to, etc.)
Genitive: Possessing sth. (Henry's, his, of the United States, etc.)
*note that nominative uses linking words and accusative/dative use action verbs.
If you look in the sentence we have here, been is a paste tense of to be.
It is describing the subject as being one of Henry's favorite board games, and is thus using the nominative.
However, the term predicate nominative is a bit more specific than that, it's not referring to that entire phrase. It is just the object of that predicate, what the subject is being renamed to. Usually you can substitute equals in the sentence and it should still work.
In this sentence, the predicate nominative is games. (Chess = game)
