Right. An operation is idempotent only if doing it twice has the same result as doing it once. If you have to worry about whether an operation has already been done, it's not idempotent. If you have to worry about order of operations, it's not idempotent.

What's being asked for here is eventual consistency. If you make the same request twice, the system must settle into a the same state as if it was done only once. That's the realm of conflict-free replicated data types, which the article is trying to re-invent.

   x = 1

is idempotent.

   x = x + 1

over a link with delay and errors is a problem that requires the heavy machinery of CRDTs.