Honestly, that sounds like it's still the Gestalt principles at work. Did you read the link I posted about luminance?
The person who made that art seems to have a keen eye for color design. The colors are chosen in such a way that the signs "pop", making them look like they're well away from the wall despite being a grid of colors on a 2d plane. That red especially looks bright relative to the rest of the image.
There's no way they could be hiding anything special in a static image to give it a parallax. Your brain is doing all the hard work for the artist.