I'm not sure about the theory that during the N64 and GC eras Nintendo was less Nintendo-like or that they were desperately trying to go after the "hardcore", "mature" demographic with those consoles. I don't think Zelda: Wind Waker would have looked like it did if that were the case. Or that a game called Super Mario Sunshine would have been released. Or that the GameCube would've been purple. I think those consoles were just as Nintendo-like as any.
If such a thing exists, surely the Wii is less Nintendo-like as its success is built on Wii Sports and Wii Fit, ie. realistic, simulator, "lifestyle" type games, instead of Nintendo's traditional character based, fantasy based, story based, action/adventure based games.
If a company abandones its flagship game, than that surely counts. Would Sony or Microsoft still be the same without Gran Turismo or Halo? Of course not, something would be missing. Just like 2D Mario. Then there were things like the Resident Evil series going Gamecube exclusive. It's not like Nintendo stopped being who they are completely, but they definitely weren't the same as they were back in the NES days or nowadays with the Wii. Another example would be Nintendo trying to inject more story in their games, following the industry instead of going their own way.
The Wii's success is built on Wii Sports, Wii Fit, 2D Mario and Mario Kart. There seems to be a balance between new and old when it comes to the biggest games on the system which would explain why the Wii broke sales record after sales record. But actually, only Wii Fit is really new. The NES also had plenty of Nintendo sports games like Tennis, Golf and Baseball.