It seems that the demo you shared utilizes a canvas library known as Clay.js, which is not something I am familiar with. When it comes to 3D in canvas, the popular choice is Three.js, as you mentioned earlier. One advantage of Three.js is its support for webGL, a browser-based variant of OpenGL.
While Three.js has somewhat limited documentation, there are some examples available. However, apart from some books, there isn't much hand-holding, and you'll need to dive in and start coding. Here are some online resources that might aid you in getting started (not all specifically focused on THREE.js):
To simplify working with THREE.js, Jérôme Etienne introduced a project called tQuery, akin to jQuery. It serves as a wrapper to facilitate hands-on involvement. Check out this video where he demonstrates creating a webGL game in just 10 minutes.