I have Apple TV 4K and 2 other Apple TV series 1 and 2, Chromecast and Amazon Fire. It will work on your Apple TV 4K after you upgrade to the lattest OS version. A new app will be displayed and then you can see on your TV.
However on the rest of the devices I haven't been able to make it work. Fire TV will download Apple TV but I didn't see the Fitness + so no luck there. I tries to screen mirror the iPhone screen to the other devices (Chromocast, and Apple TV series 1 and 2) and it won't mirror the display. I guess this is typical Apple. They want us to buy the latest Apple TV to be able to see on a TV. Using a Cell Phone to follow the instructors doesn't work. Can't concentrate to see the person and do the exercise.
Thanks Apple but don't appreciate to have to spend another $200 to see on the screen.