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.
tvOS 9.2.2, like tvOS 9.2.1, is a minor 9.x.x update, focusing on bug fixes and performance improvements that aren't immediately obvious. Apple's release notes have suggested the update includes bug fixes and security improvements, and no outward-facing changes were spotted in the first three betas, but this post will be updated if we discover any new features or fixes in the fourth beta of tvOS 9.2.2.
Apple is also working on the next-generation version of tvOS, tvOS 10, which includes new Siri features, single sign-on cable authentication, and more. tvOS 10, currently available to developers, will be released to the public in the fall.