No, it doesn't. Apple Support can't figure this out either. It is like no one has ever used the service before. The only thing that works is charging me for the service. You can't actually play the workouts on Apple TV, or even find them on iPhone. The way the Watch interacts with Fitness+ is a total mystery. Apple support just transferred me from person to person and finally gave up.
The article you linked to says, for instance:
If you own an Apple Watch, Apple Fitness+ automatically appears as the center tab in the Fitness app on your iPhone. For iPad, the Fitness app is available for Apple Watch users to download from the App Store. The Fitness app is also available on Apple TV.
However, there are no tabs at all on the Fitness app on my iPhone. It is true that there is a Fitness app on my iPhone and iPad and Apple TV. However, you can't play the workouts on the Apple TV, you can't pair the watch to the Apple TV (if you are even supposed to do that), and you can't even look at the workouts on iPhone.