Well, there is hardly any plot to either the Zelda Game Watch or the Zelda Game & Watch. Link just kills dragons with a tomahawk to save Zelda.
They were based on the original two games and back then there were no multiple links, which automatically makes them sequels to LoZ and AoL. They were basically just Zelda merchandise and didn't have any impact on the timeline. The developers of future Zelda titles have also completely ignored them which means that they were never meant to be nothing but merchandise. In my opinion the same applies to Tingle RPG. We can use it to better understand Tingle, but that shouldn't be something to base a theory on.