Let me preface this by saying I didn’t do well in chemistry. I haven’t gotten any better at it over the years, so I could be looking at this entirely wrong.

It sounds like these Maxwell’s demon enzymes do the catalysis, which causes enough of a change in their shape that it changes their mobility until they return to their original shape. That temporary conformation gives them better motility. That pushes them away from the products of the reaction, preventing the enzymes from reversing it when things calm down.

When a system’s at equilibrium, that reaction would reverse as often as it proceeds, so this is the big deal part. By moving the enzyme away from the products, Maxwell’s demons ensure the system doesn’t remain at equilibrium without needing to use any additional energy. They don’t need to kick off a wall to swim away.

It’s like how you’re not supposed to wear the same bra two days in a row because it wears out the elastic. After having been stretched over your body all day, the elastic stays stretched for a little while and takes time to return to its original shape. It’s not magic, it’s just a property of the material.