Yes, sadly I rolled my own engine directly on top of Java/OpenGL, rather than using something pre-existing. (There were some decent reasons for it considering how specialized the visuals I'm working with are—but it was a big mistake over all. Should've done it in a more prototype-y fashion).
To code the animations I use something in the engine which resembles CSS transitions and can be attached to arbitrary Java objects, which I call 'property modulators'. So most of the animation you see comes from setting up one of those on one property or another.
Most of the rendering code would be a pretty direct port—I don't think I'm using anything from OpenGL that isn't supported by WebGL. That said, it is a desktop Java application and it would be non-trivial to port it to javascript. And that said, it probably would've been best to do it in javascript in the first place, but I did basically no web dev when I started, so... shrug
