This is a bit complex because of the way people define own.

Technically no one but the company who developed the games own the game.

Publishers effectively own it as they usually monopolize the entire licensing control of the game.

Gamers never own but merely have the license to play. This is true even with games from long time ago. While you do own the physical disk, you only license the data inside the disk.

Some people may define ownership of a game by the fact that no one is going to take it away from you. In that way, gog does do that. Since you can download a DRM free version you can install as many times as you want for as along as you want.