If you did like the link, and had each 2D image pointed along a radial, then having a single slit somewhere in the table would work decently. But edge lighting of acrylic really works best when the light is flush to the surface of the acrylic, so it would still not be quite perfect.
You would want your light to be a strobe, matched to the frequency at which your acrylic frames pass over the slot. The video doesn’t really need a strobe effect since the 3D print gives a continual line between frames, which serves to enhance the quality of the animation.
POV (persistence of vision) is pretty easy, and quite well understood. The only difficulty really is making the electrical connections from the rotating platform to any stationary components (I would imagine most people just opt to make everything rotate).
So, just mount LEDs for each of your frames, and use a single chip Arduino type microprocessor to control LED timing. You could embed a sensor to pick up on the rotational speed of the platform, or just measure the rotation of the platform and program that in after an initial trial.