I'm not 100% familiar with the Nintendo story. What happened, anyways?
Nintendo shattered their chance at the 64-bit market by using a high quality but dreadfully slow polygon engine in the N64, and tied it to ROM cartridges for piracy reasons. They practically handing the market over to Sony, who had very low license fees. Nintendo haven't really recovered -- or changed their business model.
Gamecube is a terrific piece of engineering, far better than the haphazard PS2, but Nintendo's licensing scheme is still their undoing. If not for Game Boy Advance and DS, they'd be in big trouble.