Playing Purchased Movies

Hi all.

Yesterday I had a problem with my Internet connection that lasted 2 days. It was a provider problem.

The router was, of course, unable to connect to the Internet, but my local WI-FI was correctly working in my home.

I have purchased and downloaded movies from iTunes; I have added all of them to my TV App on my MacBook

I also have AppleTV connected to my TV and, over WI-FI, I was able to access the MacBook library and browse all my movies.

The problem was that when I try to play one of them over wit-fi, it says that AppleTV can't play that content. It happened for all my movies.

Do I need an active internet connection even if I want to see them on my local wifi?

Is it not enough that I'm logged with the same account on all devices?

I was still able to play a movie locally on MacBook without internet connection, but not if I try to stream across my wi-fi on apple tv

Thanks