So the hard part of this isn't computing the reflection color (that can be done with an environment cubemap and some math expressions), but sorting the transparency. This demo uses "depth peeling", which is a fancy term to just mean rendering the model in a few different frustum slices along the view direction, and using the previous framebuffer content to accumulate reflection.

The whole purpose of this trick is to abuse the rasterizer! I struggle to see how compute shaders would make this faster.