Ehhh...? I mean, that doesn't really make him a video game character, just a videogame-themed cartoon character. It kinda puts him on the same level as say, a character from that new GlitchTech show (granted, Captain N does have the advantage of being affiliated with legit game licenses and what have you).Captain N isn't allowed because he's not a videogame character.
He's a character that was sucked into videogames, hangs out with video game characters, fights videogame villians using videogame equipment in a videogame world and is directly owned by Nintendo.
A 1st party character who's entire existence revolves around videogames isn't videogame enough for you?
Also for clarification I'm pretty sure Captain N is a DiC-owned character. Not entirely sure who owns him, but he's certainly not first-party.