The tvOS 11.2 public beta can be obtained by going to the Settings app on the Apple TV and navigating to the Software Updates section under "System." "Get Public Beta Updates" will need to be toggled on, and once it is, the Apple TV will download the beta software.
According to Apple's release notes, the tvOS 11.2 update enables a new AVDisplayManager feature for developers, designed to allow the device to automatically switch video display modes to match the native frame rate and dynamic range of video content.
The update includes support for switching the Apple TV 4K display output to SDR for apps that are GPU-bound when running in HDR and it re-introduces the Unwatched category in Home Sharing for Movies, TV Shows, and Home Videos.
Apple says tvOS 11.2 also adds new features, bug fixes, and security improvements to the tvOS operating system.