Ok sorry about that, I'll make an attempt by clipping paragraphs from the linked page. My trepidation about putting it into my own words is primarily about being responsible; I was a physics major but dropped out of school to join the work force before completing my degree.

The defining characteristic of a reversible process is that it can (or could) proceed equally well either in the forward or the reverse temporal directions.

"Newtonian processes" are primarily about objects moving under a system of forces, such as gravity. We describe their motion as occurring between two times (essentially the beginning of the gif and the end). The OP's gif created an effective illusion because in general, nothing that happens when describing motion could not happen the same both forward and backward.

If you get your car into a tight parking space, you can get your car out of the tight parking space. It may seem to us as if the car is stuck, but we know that if we simply reversed the exact process used to get the car in, we will also get the car out.

Lighting a match on the other hand, is not a Newtonian process. It's a chemical process and not (necessarily) reversible . If we were shown a film of a match being struck against the side of a matchbox, where it then flares up after being dragged across the striker, no one would be fooled when the clip was played in reverse, because a flame spontaneously settling down, the blackened match-head regaining its red color, the stick going from charcoal black to wood again, makes absolutely no sense. It's a chemical process and not Newtonian.

The equations physicists use to describe motion under the influence of forces also do not care if we are starting from the beginning and working forward, or starting from the end and working backward. The math is the same.