Can't find bought video in web browser

I bought a comedy video (Comedy Central Roast) with my iPhone.

I want to watch it on a big screen (windows computer) in a normal web browser (Chrome).

I can find and play any Apple TV + movie there ... but not my bought comedy video.

It appears in no category. There is no search field and I have no access to the "up next" list - where I put my video to.

How can I find my bought video in a web browser?

I only can find it running the apple TV app on my iPhone.