GOG Connect is an intriguing initiative aimed at bringing your Steam games over to GOG, provided they exist in its catalogue and the developer has agreed to take part.
In theory, you connect your Steam library with GOG here. It scans your collection and adds any qualifying games to your GOG library for good. It's a time-limited offer—for the first wave you have around five days to complete the duplication process. "Why buy them more than once?" the tagline goes.
If the game ends up being removed from your Steam library (for example, if you thought to try a sneaky refund and keep the GOG copy), GOG reserves the right to delete its version too.
The problem is, Connect doesn't seem to be working right now. Team PCG have hit issues from a simple "something went wrong" to a number of eligible games not being picked up by GOG.
The FAQs state that the Steam API used to provide library data can only handle a certain number of calls per day, after which you'll be placed in a queue. It may well be out of juice.