tvOS betas are more difficult to install than beta updates for iOS and OS X. Installing the tvOS beta requires the Apple TV to be connected to a computer with a USB-C to USB-A cable, with the software downloaded and installed via iTunes or Apple Configurator. Once a beta profile has been installed on the device through iTunes, new beta releases will be available over the air.
As a minor 9.x.x update, tvOS 9.2.2 is likely to focus on bug fixes and performance improvements to address issues discovered since the release of tvOS 9.2.1, and Apple's release notes do say the update contains bug fixes and security improvements. Any outward-facing changes found in the tvOS 9.2.2 beta will be included below.