"Compound nominal predicate" seems to me to be a term invented by Russian English teachers, but it is really quite easy to understand. If we think of the structure of a sentence in English as consisting of a subject, a verb, and (sometimes) an object (in that order), then the compound nominal predicate is really the verb and the object together.
The text above also refers to the "predicative", which is really the object. As it points out, objects in English can be either nouns or adjectives. (Apparently, objects in Russian cannot be adjectives.)