Some might think a predicate nominative is used in this sentence. But nominatives are only used when there is a linking verb, "to be." An example of predicate nominative is: "This is he." Another example is: "It is I." With the verb "to be," the object is in the nominative case.
In the above example, the verb is "included." Therefore, the sentence does not use a predicate nominative. This simply means that the object of the verb is in the accusative case. So, the sentence should read:
"Famous guests at the banquet included Archie, Ray, and him."
This is actually a very straightforward question. To simplify things, you can write, "Famous guest at the banquet included him." "He" would not work at all, because it is used as a subject pronoun.