You've quoted from the "Concepts" section. About the Concepts it says:
This Clause describes concepts that are, for the most part, specified precisely in other parts of ISO/IEC 9075. In any case of discrepancy, the specification in the other part is to be presumed correct.
Elsewhere it also says
NOTE 299 — Although ROW_NUMBER is non-deterministic, ...
The intent is pretty clear. ROW_NUMBER is non-deterministic. In case of a tie, it assigns sequence numbers to the tied elements in arbitrary order.
(That is the only difference between it and RANK. "RANK ... ORDER BY ()" would return 1 for all elements and therefore be useless; "ROW_NUMBER ... ORDER BY ()" or equivalently "ROW_NUMBER" assigns unique sequence numbers, and that is useful. For example you can use it to delete all but one copy of duplicate rows in a table. And it sounds as if Postgres botched it, and implemented ROW_NUMBER as if it were RANK.)
Quite a few parts of SQL are non-deterministic. I mentioned LIMIT without ORDER BY earlier. And even ORDER BY is non-deterministic if the order key is not unique.
Can we wind up this discussion now please? I'd rather see a patch with an implementation then spend more time arguing like lawyers or religious scholars.