Priest's Smite has a hammer icon, a hammer is more of a holy thing in general since priests use maces as well. Regardless, if you classify a paladin strictly as "someone who uses holy magic and wears heavy armor" then yes, he's a paladin. However, he's more of a "cleric" who's not fully a priest but not entirely the marital warrior that most paladins are. He doesn't fully capture that image of weapon skills like Uther, Tirion, or even Arthas did.
That's why I said if he trained with someone like Muradin he'd become an unstoppable paladin considering how much raw power he has in the light. Perhaps he'd be more powerful than someone like Uther if he trained consistently.