So far, correct me if I am wrong, the state of the art prior to this would be something like Unity's Mecanim, where you define a state machine for animation transitions, which would interpolate animations to save you work.
Very handy for character locomotion, but only gets you so far. I'm not sure how applicable offline processing is to this though, since if you have a large number of different types of obstacles to be traversed, you'd have to bake >= that number of animations, and your animation state machine would be enormous. The end goal might be to do that in real time, but I don't think anyone is going to seriously suggest running a neural net to calculate animation positions while the game is running. Maybe if you had some smarts in the level designer you could determine the potential pool of animations needed based on placed geometry, and build the animations at packaging time along with the state machine.
If that is still not enough, they can also try to look at ways of producing a "good enough" effect with a smaller network.
Then, it can also be limited to only some characters, the ones that you are more likely to pay attention to.
Now, the MS Kinect does some intense processing behind the scenes (random forests) to capture your motion in real time. Yet you can still run games with decent performance. I think a neural network to adjust animations is not too dissimilar in terms of performance cost.