The article doesn't propose anything especially different from Lamport clocks. What this article suggests is a way to deal with non-idempotent message handlers.
Its true that idempotency can sometimes be achieved without explicitly having message identity, but in cases it cannot, a key is usually provided to solve this problem. This key indeed encodes the identity of the message, but is usually called an "idempotency key" to signal its use.
The system then becomes idempotent not by having repeated executions result in identical state on some deeper level, but by detecting and avoiding repeated executions on the surface of the system.