"olfactory based illusion detectors activated!"

That butt smells like plastic, time to move on.

Also, that Pacman can spit into gun barrels.

Same way as lenticular animation (which is basically the same thing except it's using refraction instead of masking stuff with vertical bars). The frames are cut into vertical strips and arranged so that as the mask moves across the paper, you can only see the strips that make up one frame at any one time. More or less.

Short answer is there's software that does it.

the images on the paper aren't actually moving.

Yeah, I guess. This just seems like rather obvious animation. Does a flip-book count as an optical illusion?

yes. animation is. I suppose all optics are illusion...if you think about. *bong hit*