I was under the impression movies were distributed on encrypted physical media which the key was made available on the release date. Maybe things have changed.
I recently went to a small theater to watch a movie. It didn't start. After 10 minutes I went to talk to a manager. They had forgotten to download the licensed movie for the day and that download would take a couple hours. I had to get free passes to come back another time.
Sounds more like they forgot to transfer the movie from their central server to the screen server. Normal workflow has been to get the physical media via courier to the theatre, staff then transfer the content to a storage server and then a courier picks up the film and delivers it to the next theatre.
edit: A normal DCP (digital cinema package) is around 100GB, bigger if it's 3D/4K/Atmos. Some of the biggest packages can be 500-600GB with all versions (2D, 3D, dubbed, hard of hearing, atmos, auro, DBOX and so on). So not really feasible to download that via the Internet in a couple of hours.
The films are encrypted, but the distribution media isn't necessarily physical. It depends on where in the world you are, but it has been pretty normal to distribute films via satellite, but recently Internet speeds have become fast and cheap enough to allow films to be distributed via the Internet.
