It “installs” instantly. My guess is they have each game already installed in immutable volumes on their SAN and simply mount the volume for whatever title you want to play.
Again it comes back to the software license and ToS. The question is whether owning a license entitles the user to run that software anywhere they want. I can’t imagine that’s ever been tested in the courts, and to a layman it seems reasonable that Bethesda and Blizzard would be laughed out of the courts, but I’m certainly not a lawyer.