Captain Rainbow is very quickly revealing itself as more than a top-down, adventure-based take on the same Japanese superhero tropes explored in Viewtiful Joe: it's a haven for lost Nintendo characters.
The first video introduces Little Mac and his unfortunate weight gain. Little Mac then tells the story of Birdo, who seeks popularity with the boys (Yes, Birdo, or as she used to be known, Catherine, is female. Yes, we read the Super Mario Bros. 2 manual.) In the second, Nick (who becomes Captain Rainbow) trains Mac back to prime littleness, with narration from Nazo no Murasame-jou's Takamaru (who will probably be the subject of the next video).
We didn't embed the videos because it's in your best interest to go see them on YouTube, where the clever uploader, 23Makoto23, has used YouTube comments to create subtitles (here is the original Captain Rainbow video subtitled).