If the game was originally released by a company that provided a physical release of the game, or even if the authors preferred to release it officially by a third-party website instead of themselves, then that's the publisher.
Otherwise, the authors decided to release it themselves (or under a company name they created). In this case, that's the publisher.
The original publisher should never be empty. Whenever it's currently empty, it just means we didn't identify how it was released yet.