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?
ExtremeTech is the Web's top destination for news and analysis of emerging science and technology trends, and important software, hardware, and gadgets.

How to Use a PS4 Controller on Xbox Series X or S

Compatible With Microsoft Xbox 360, One,Nintendo Switch Pro Controller,Sony PlayStation 2, 3, 4 Enhance your gaming experience with the high quality controller thumbstick caps. Prevent your fingers from slipping and provide more accuracy and sensitivity when you play video games. Protect the analog sticks from long term wear and tear. Made of silicone material to improve grip, performance and comfort.

Insten 4pcs Thumb Grips for PS4 Controller Xbox One Xbox 360 Sony PlayStation 2 3 4 Controller Analog, Red

PS4's DualShock 4 is compatible with next-gen Xbox Series X games

Xbox 360 to PS4 Super Converter (Light Green) for Windows, PlayStation 4

Xbox One vs. PlayStation 4: Controllers - Neoseeker

8Bitdo Retro Receiver for PS1 PS2 and Windows, Compatible with Xbox Series Controller, Xbox One Bluetooth Controller, Switch Pro and PS5/PS4 Controller

Microsoft's Xbox One vs. Sony's PlayStation 4

Protect your joystick from dust and scratches. Xbox Series X/S.

Controller Thumb Grips/Caps - PlayStation 4 Xbox One Switch Xbox 360 PS4 PS3 PS5

10 Reasons To Choose Xbox One Over PlayStation 4

iPhone, iPad, and Apple TV Gaining Xbox One and PlayStation 4 Controller Support - MacRumors