Although not highlighted at the WWDC conference, the latest beta of tvOS supports picture-in-picture mode on Apple TV, according to 9to5Mac.
PiP on Apple TV
The code has actually been in tvOS for quite a while but it seems that Apple has been waiting for something. That something may be the new TV app that supports picture-in-picture functionality starting with tvOS 13.
With picture-in-picture you can place a small video window in the corner of the screen whilst navigating the menus and other apps. It appears to work in the same manner as the picture-in-picture mode on iPad, with some basic controls in the window. Here is a short video.
It is unclear if PiP is a system-level feature that automatically works with all video in tvOS or if it is an optional API that developers can take advantage.
The new functionality was spotted in the second beta of tvOS 13. The upcoming tvOS software also will also include new announced features such as a redesigned home screen with video previews, support for Xbox and PlayStation controllers, multi-user support, new 4K HDR underwater screensavers, and more. Learn more about tvOS 13 here.
Apple will release tvOS 13 as a free software update for Apple TV HD and Apple TV 4K this fall.