Innovation is often a trade off for depth, since if a game requires a player to do something so brand new then teaching the player this replaces challenging the player with further exploring an old concept. So while doing something different can be a good thing, the further away from concepts that have already been explored you go, the simpler and shallower your game becomes.
There are two classic inventions: something that solves an existing problem or the unique combination of existing ideas. When inventing to solve a problem in a game, you are still building on an existing type of game. Mirror's Edge for example is a classic action game, like Mario or Sonic, but it tries to solve the problems with doing action/platforming from a first person perspective, mainly through allowing the player to see their own body from that point of view.
Its also important to consider a game is a piece of art and not a tool. No niche in art is ever completely filled, and it makes no sense to avoid something that was done before if it fits with the game you are trying to make, and if what was done before was a good thing. Imagine if film makers stop making Zombie Horror movies after Night of the Living Dead because it had been done before - I mean sure its great that we have Zombie Hack and Slashes, Zombie FPS, Zombie Adventure Games, Zombie Sandbox Games, Zombie RPG's, Zombie Sport Games ...but you know, we can still make another Zombie Horror Game. Like the films, there is a lot of ways you can handle this concept to give an audience a new perspective.
I think innovation gets a lot of clout because first, technology folk are involved and really like that sort of thing, and second because gamers complain about games seeming too repetitive and similar. However, its important to put that complaint in context that it's often because games remain so simple and safe that the experiences all bleed together, and adding some gimmick is not going to fool most players. Changing things that will effect the player's experience are often very simple, but at the core of what you're planning to deliver to them.
Here's a fun lesson in innovation, the first party RPG came around 1986-87 -how long do you think it was until RPG's have battles where each unit in the ally/enemy parties took individual turns while everyone else waited? I mean that's the game play most people think of when someone mention a JRPG. And it only took, oh, about 10 years to come about. This came after many RPG's that had combat when units did not wait to take turns and could even free move around battle field with no pause. But turn base combat allowed for greater depth in the interaction of timing and turn advantage, and fuel so many ideas that it became the new standard method of play. Of course, no one thinks of turn base combat as an innovative idea, even when it came out. And the best invention to game play, the things that will revolutionize genres, are often just as subtle as that. You feel like it should have been there all along, so you don't get shocked when it appears.
The last bit about invention and creativity is that innovation does not overcome limitations, in fact limitation help people invent new ideas because it gives them something to focus on. Stealth game play was made cause old system couldn't handling too many smart enemies on screen. Horror games came from the uncanny valley of graphics in that generation, not to mention its use of load time and limit field of vision were both inspiration for furthering tension in these games. Tetris even came about because Alexey Pajitnov could only fit in seven shapes into a game. The less a creative person has to work with, the more interesting they use what they got. Audiences do not want innovative art, they want interesting art. Innovation becomes ordinary, interesting is timeless.