What is the secret way that martial artists walk over rice paper with out damaging it?

Probably even weight distribution, the opposite of tip toe. Slowly place the entire foot and slowly apply weight as evenly as possible, and slowly shift weight from foot to foot when taking the next step, and lifting each foot, so there are no concentrations of force in time or space.

There are many other tricks and feats and techniques and so on.

You can’t know that until you have learned, Grasshopper.

As you step, you crush, not twist.

You become the rice paper, then you will not harm it.

You become the coin, then it becomes part of you and free of hands.

You make certain your feet are very dry.

I’ve tried it.
For fun.
It never works.
For me any way

That requires exceptionally excellent balance. A man I know walks on rice paper every day and walks tightropes as well while doing katas. The office where he works has a nightingale floor that makes much noise when the other employees walk around it, but he walks there silently. No one can understand how he is able to do that. His balance is unshakeable in martial arts bouts. No one has ever been able to knock him down.