Text on the website is a combination of SVGs and real characters which are then transformed using CSS. Assets are from /assets/doodles.json which contains information on how they can displayed and animated on a canvas through WebGL using a custom engine from /assets/js/engine.min.js.
It's WebGL. Doesn't look like any library/engine I'm familiar with, quite likely custom.
If you're interested in more detail, you can run spector.JS on the site to capture the render calls of a frame.
It's from Nintendo, wouldn't be surprised if they hired some of their creative team and developers to work on it.