The speaker owns more than one dog, because Zeus is a restrictive appositive. This can be concluded about Zeus
An appositive noun or phrase is restrictive if it narrows the word it modifies. It says which of the nouns you are writing about. A restrictive appositive noun or phrase is necessary for the meaning of the sentence.
Here is the example of restrictive appositive:
My best friend John loves eating burgers and pizzas
Hence, the correct answer is The speaker owns more than one dog, because Zeus is a restrictive appositive.
