And this, my people, is why the Nintendo Direct hype threads are a spectacle by themselves.The answer, for me anyway, is that since the GBA/GCN years (if not beyond) Nintendo has cultivated a base that was not at all well served by where the rest of the industry wanted to go, and where the other major players consensually decided was the future of video games. Entire genres, paradigms, design priorities, and ways of thinking about games were abandoned or derided as old-fashioned; entire experimental avenues of design research were dismissed as gimmicky, the wrong way forward, and not the consensus future. And if you disagreed with this, Nintendo welcomed you back with open arms with a library, old and new, that promised there could be another way. They built a relationship of trust where fans willing to play along with Nintendo's craziest impulses felt rewarded over a long run, even if not every experiment was well received.
I also think SSB Melee played a much stronger role than people realize in forming such a thing as a coherent Nintendo identity, in that it drew the disparate tribes within the base to each other's series that they might not otherwise have tried, familiarizing them with the characters and music. There is such a thing as a Nintendo subculture in the form we know it now, rather than a Metroid base and a Fire Emblem base out on their own and chasing whichever platform scratches their itch, because the fandoms within it cross over to each other's games. Brand recognition is for Nintendo rather than just Mario or Pokémon, and it means something more than just the shared publisher or platform, pointing to a broad but vaguely shared understanding of what a video game is.
There's a lot more I could say about this, but perhaps this isn't the place to really dig in.
Would just point out that is wasn't just Melee, it is the entirety of the Smash series.