I just do not see much value getting it "for free" because on sale it is almost free.. even on GoG (3-4 currencys), but indeed every game in this term got a unique key and in theory could be tracked. However, as there is no online activation i assume there is no limitation on the amount of "activations" and backup is no issue.
Manually you can do nothing, in term the key is missing... unless some sort of crack used, because the game got a unique ID generated, stored in a encrypted condition.
I do not truly enjoy but not sure it can be considered a real DRM.
I think, once the key is saved and game fully installed. You basically never have to insert the key once again, thus most likely saving you the hassle of a new input at every new install. However, you may have to backup the install-files with the key-infos, or even the whole game.
Besides: The current Steam-Version is basically equal to the GoG version, including key-demand. It can be started from the exe only, but this is a rare exception, especially for a franchise. However, GoG is the only independent shop providing this "fully capable" Doom 3 version; all the other shops are basically "Steam-providers"... somewhat funny. https://www.pcgamingwiki.com/wiki/Doom_3
So either get it on GoG or... Steam as the only other option.