It's fake 3D! It's based on a hand-drawn frame by frame sprite animation. Reaktori drew the art for it and programmed the initial implementation.
The die sprite looks like this:
But then it's also rotated so it'll look something like this (this gif here is a bit janky, sorry):
Then on top of that die sprite we draw the faces of the die. The faces are just static sprites and they're drawn on the die 1) positioned and scaled depending on which side of the die it's on and which frame of the die animation is currently being drawn, and 2) rotated to the same angle as the die.