PS4 DualShock 4 controller is compatible with the Xbox 360 - Xbox One next?

We recently learned that, this generation, the PS4's DualShock 4 controller would work with PCs out of the box, unlike the PS3's DualShock 3. Now, a video has surfaced that shows the DualShock 4 working with the Xbox 360. If the video isn't staged in some way, does that also mean the controller is compatible with the Xbox One?
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