Not really, if the game is DRM-free (which is the case for all games on GOG and even some on Steam, plus the Steamworks DRM that most games use is very easy to

Not really, if the game is DRM-free (which is the case for all games on GOG and even some on Steam, plus the Steamworks DRM that most games use is very easy to bypass if there's nothing else in addition to it), you effectively do own it. Of course, it's your responsibility to preserve a copy of the files because your ability to redownload them in the future isn't guaranteed, but once you have them, nobody can stop you from using them.