There's a fatal flaw in this scheme: the person who accepted a bribe is now in position to extort money from the briber forever.

I've never heard of laws working in the way I will describe, but I've got a better algorithm.

The crime is this: to (1) participate in bribery and (2) to not be the first party to report it to the authorities.

Immediately that the bribe has occurred, a race initiates between the two parties to be the first to register it with the authorities. The bribe money becomes prize money to the winner, with the loser facing consequences.

Yeah but this wouldn't address the key problem outlined in the article. The issue this is trying to tackle is that of people being forced to pay bribes for things they are legally, perfectly entitled to. The corruption this is aimed at is the corruption endemic to the civil service/government that it's impossible to avoid in everyday life.