Online console gaming was pioneered by SEGA, with Microsoft introducing Live after that, very heavily based on SEGA's online infrastructure.
When they upgraded the Live structure for the 360, they took systems that were already active and popular on PC and just ported them into the system. There was zero innovation here.
The achievements system already existed too; however, Microsoft DID have the unique "innovation" of requiring achievements for all games, and tallying them all up in one account for all games played. But that's most definitely a secondary aspect of gaming.
Nintendo made motion sensing a permanent part of all three console makers' hardware, and I believe also heavily influenced the decision to include gyroscopes and accelerometers in smartphone design. Motion sensing was also not original to the Wii, but the method with which they decided to implement it was, and their influence in releasing motion sensing absolutely changed the face of gaming forever.
Nintendo also created Miiverse, which AFAIK is entirely original, and applied it to all Wii U games. Every game is required to implement Miiverse, though they can do it in a variety of ways, and some really do it creatively. And I feel that it definitely changes the face of gaming on the console a lot more than most would realize.
There's absolutely no debating who made the biggest innovation. The most, numerically, though, is a much more difficult decision, but I still feel it'd be Nintendo.