We got the word directly from Microsoft. From now on, all apps must offer Kinect support in some form (and it may be optional for users). We were told by a representative, "With the new dashboard our objective is to bring the power of Kinect functionality to every experience where voice and gestures make sense." Controller support, obviously, won't be abandoned, but Microsoft wants to insure that "consumers can simply use gestures, voice and their controllers in a seamless way."
[Update: Adjusted the post to make it clear that support is required from developers, not users.]
Microsoft Xbox One