Potzato: For instance on gog, there is a DRM on getting the installer of the game you bought (you want the installer for the game, you have to log on gog which has nothing to do with installing the game).
Once the game is installed, you play it on your computer without anything else = DRM free game.
Edit : To be clear, I even consider putting ads in a free game some kind of DRM. And I am not against all forms of DRM (under my wide definition)
I'm aware that you mean to say the games on GOG are DRM-free after download, but I don't see much use in a definition that applies DRM to the act of purchasing. By that definition the process of buying a paperback on Amazon involves DRM, and maybe even the process of buying a board game at a board game fair (you had to pay an entry fee, which has nothing to do with playing the game). As you say, the act of purchasing has nothing to do with the product, and therefor it should be viewed independently of the product's properties.
On the other hand, I'd also change your definiton:
Once the game is installed, you play it on your computer without anything else = DRM free game. to:
Once the game is downloaded (or, in the case of retail, bought), you can install and play it on your computer without anything else = DRM free game. Because the process of installing a game can very well involve DRM and prevent you from playing it in the future, even if system compatibility is still given (see one-time online activation or client dependency for installation).