Nintendo is the publisher, yes. They also publish games from other developers (e.g. Bayonetta 2, Xenoblade Chronicles).

Their other tentpole franchises are mostly developed in-house (Zelda, Splatoon, Mario Kart), via subsidiaries (Retro Studios) 2nd-party developers (GameFreak - Pokemon, Intelligent Systems - Fire Emblem), or 3rd parties (Bandai Namco & Sora - Super Smash Bros).