GoG had already started a similar program in the past. It was called “Reclaim Your Game” or something like that and it allowed you to enter in game keys for supported games to claim a free DRM free copy. Now, as if to take it further, they are now running a Connect program which allows you to link ONE Steam account with your GoG library. Connecting your Steam account will allow them to grant you free DRM Free copies of games you already own on Steam. Check it out:
GoG Connect: https://www.gog.com/connect
GoG Reclaim: https://www.gog.com/reclaim
Im not sure which Steam account to use yet. My lesser accounts are the ones with most of the Indie games on them but Id much rather connect my main account. (I created them before Family Share).