Your average techie can get around that by using Jellyfin, Sonarr/Radarr, Torrent trackers and such, but the military has to follow the law.
THe fact that ships travel around the world doesn't make this easier. Even if the Pentagon could make a deal with most of the major U.S. streaming services to provide their content to the military in a secure, offline fashion, which they probably could, those companies are often prohibited from distributing that content outside U.S. borders due to exclusivity agreements.