How do these 3D illusion lights work?

I clicked on one, and it says this:” From afar, you will see the design, but as you get up close, you see a thin acrylic glass sheet that’s completely flat.” So it’s most likely a design within the glass. Here is a video

It a picture etched onto a flat piece of plexiglass. The etching become visible when you light it from the edge.

The video from your linked page makes it apparent. Skip to 1:00.

Google image search for edge lit sign also gives helpful pictures.

Thanks guys.