What is the Toilet Paper over mode in the games video settings all about? Does anyone know?

I think it's a joke that while the game was in development someone complained (thanks internet and OCD people) that in one of the screenshots of a toilet the toilet paper roll was inserted the wrong way. You know, some people put it with the new sheets to the outside and some towards the wall. So that option is a way for the developers to make fun of this.

I think this is what happened but I'm not sure.

You're absolutely correct on this one. It's just a little joke and has no effect on any riddle/puzzle in the game.

Tick that option while you are in the toilet room, and you can see this change on the fly.

I tried toggling the option in a hotel room, nothing happened to the paper roll there. It could be a reference to the useless options in Monkey Island settings (at least The Curse of Monkey Island had one as far as I remember)

It only works in the toilet that is completely dark (with some glowing red "eyes" on the right side).

Unless, you use the light switch that is.