Switch aiming for the classic gamer is something that was noticed before it launched, at least by those who didn't strictly rule out that possibility.
Breath of the Wild was a Zelda game that took the original Zelda as its basis and is basically a modern version of it. I doubt that it is a coincidence that Konami made Bomberman, Capcom brought Street Fighter II and Square-Enix had Octopath Traveler in the works, all of those games being announced before the Switch launched. Nintendo had a deliberate strategy to target fans of 8-bit and 16-bit games with Switch.
By now Switch's game library offers mostly everything, so it's harder to pin it down to a single thing, but it never was only about a single thing anyway. It was only in the beginning where Nintendo wanted a clear message that they had not forgotten about the classic gamer.
The only thing that's absent from Switch are new AAA third party games, but that's something the vast majority of Switch owners don't care about because Switch's appeal is precisely that it is not like the other consoles on the market. The biggest mistake Nintendo can commit in the future is try to fit in with the rest again, because that's the surefire way to turn away their customers in disgust.