What part of the sentence implies there is a he? I don't understand.
None of them implies specifically "he", but it has to be either "he, she, it" because the verb form έχει is for third person singular.
It's probably either "he" or "she", because things that we refer to as "it" in English (inanimate objects, mostly) generally don't own things.
(But all three are accepted. Some people might refer to a young child as "it", for example, and it might own a cat.)
In a previous EN-EL question, the suggested translation on hover for "how many cats" was Πόσους γάτους. What is the difference and which is correct here?
Both are correct. Ο γάτος - οι γάτοι is the masculine noun and it is usually reserved for male cats. Η γάτα - οι γάτες is the feminine noun and it can be used for all cats. For all cats as well, can be used the neutral noun το γατί - τα γατιά.
"does he have" -- the -s for "he" goes onto the "do" helping verb in this question.
Generally, when there are two verbs in a sentence, only one of them gets the -s ending for "he, she, it", or a past tense ending, or other change, and the other one is in the dictionary form.
It is irritating that a typo in english (hr instead of he in this case) is rejected