Designed for the fourth-generation Apple TV, the third tvOS 10.2 beta can be obtained by connecting the Apple TV to a computer with a USB-C to USB-A cable, downloading and installing the software from a registered developer account via iTunes or Apple Configurator. Once a profile is installed, subsequent betas can be downloaded over the air.
Given the tricky installation requirements, tvOS betas are limited to developers and will not be provided to the public.
According to Apple's release notes, tvOS 10.2 introduces improved scrolling behavior, allowing tvOS users to scroll through large lists of information more quickly. A large swipe on the Siri remote automatically activates the new scrolling mode, and a swipe on the far right side of the remote allows users to navigate specific indexes.
It's likely there are other small feature tweaks and bug fixes included in tvOS 10.2, even though additional changes have not been specifically outlined by Apple. We'll update this post should any new content be found in the third tvOS 10.2 beta.