I believe it does. I don’t really buy many games on Itch to be honest but from what I understand and from the handful of games I have obtained from there (mostly just free games), that is indeed how it works.
And agreed. Definitely wish GOG had a larger library.
This is why I buy all my games on either GOG or Itch.
Yes, they definitely have their problems, but at least I can download an offline installer for pretty much any game I buy. Sure, GOG or Itch could still take them down in the future, but they can’t take away the offline installers I have backed up on separate external HDDs.