Sounds like a coil or capacitor in a dc-dc converter circuit buzzing, explains why its bad on the dashboard (many dc-dc converters drop frequency at low power draw levels to minimise losses, but if the frequency drops into the audible range, particularly if it hits the resonant frequency of the coil or capacitor then it can be quite loud). High power draw (in game) does the opposite.
Strange that its popped up predominantly with the Kinectless versions, but again it might be a power consumption issue, or it could be that MS rolled a minor board change along with the release of the Kinectless XB1, and so its popping up now.
[correction] seems like its been doing it for a while on some machines, not just recently: https://www.youtube.com/watch?v=skqwBNGH8VU
