It's easy to say Nintendo innovated because they were last, but check out Sega. They tried to innovate with Dreamcast, but failed to do so to a high enough degree to even begin enticing the mainstream.
No, Nintendo was able to change because they got a visionary leader. He didn't want to change the market because Nintendo was last, but because he saw the whole VG market in trouble.
And it's easy to call it all a reaction to Sony, but their reaction was to move away from what Sony was doing, and move back to their own strategy of the 80s that they had slowly wandered from. And their first move was with DS, in the handheld arena they still dominated.
And in the meantime, Sony was trying to capture Nintendo's traditional advantages by increasing their first party studios and creating their own handheld system. Those were the things that got Nintendo through the lean years, and Sony wanted them.
And lastly, the overall point is not that Nintendo ignores their customers, but that they value their non-customers just as much. They still made TP, Brawl and Galaxy this gen; their three biggest projects ever, all intended to surprise their existing customers and keep them excited.
But they know they can't grow just by competing for existing customers. So they looked for the barriers keeping non-customers from playing games, and sought ways to remove them.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
