In terms of how much it contributed the platform's success, which do you think was the most important third party title ever on a Nintendo platform, and what's your reasoning?

Tetris is thrid-party, right? If so then I’d go with that. The game was a huge contributors to GameBoy’s success, launching Nintendo into their dominant position over the handheld market.

Technically the GB version was developed by Nintendo IIRC

https://en.wikipedia.org/wiki/Tetris_(Game_Boy_video_game)

madworld. put to bed the idea that the wii is for grandmas and newborns. finally we got a hardcore game.

Final Fantasy & Dragon Quest. It made Famicom the number one system in Japan and FF esp helped popularize RPGs in the west. (not to the extent of FF7 that came years later tho). I do want to give a shoutout to Capcom tho with Mega Man. Konami with Castlevania. Tecmo with Ninja Gaiden. Series that defined third party hits like no other before it. Franchises that are still around. Even if some began in arcades like Ninja Gaiden or Haunted Castle. They were defined on NES. Final Fantasy tho is one of the earlier examples of other companies chasing that success. SEGA created Phantasy Star. Master System also got Miracle Warriors. Square helped define SNES as a RPG powerhouse. They don't get there without Final Fantasy and DQ. Now DQ wasn't popular in the west. Nintendo Power gave away the game for free. In Japan it became the most popular series there.