"Saya menghadiahkan anjing itu" would be "I gifted the dog". The word "present" means "a gift" only when used as a noun, when used as a verb "present" means more like a doing a presentation about something.
i don't thing "saya menghadiahkan anjing itu" has different meaning with the answer. It's just an alternative answer with the same meaning. Both "menghadiahkan" and "mempersembahkan" means to give something, right?