A talking penguin in a top hat moves in and the show treats it like the most natural thing in the world. That's not a setup waiting for a punchline, it's the entire show, and it works because there's nothing to prove. The sequel doubles down on the same premise: just a penguin, his friends, and a kid's house, where the only rule is that whatever happens next doesn't need to make sense.
Mr. Pen Pen II is a one-episode comedy special from 1986 and the sequel to Mr. Pen Pen, bringing the story begun in the first part to its conclusion. The earlier entry introduced Pen-Pen, the prince of Penguin Land, who wears a hat and tie. He shows up without warning at the home of a young girl named Mika and moves in along with his oddball friends. The franchise is adapted from Muroyama Mayumi's manga, which ran in Shougaku Ninensei.