Lifthrasil: Thank you! This is a great suggestion.
Not that I would be against a law suit, what GOG is doing here is false advertising in spirit. But, de jure, you are right. Their ad can still be spun as true. You still can play 'the game' without online connection, if you define 'the game' as the small part that is not DRM-ed. GOG very wisely removed the 100% DRM-free promise from their website quite some time ago. So as long as a small part of the game can be played offline, they will get away with it in front of a court.
The first course of action is to contact the seller, GOG, to have them sort it out. In case someone purchased it unaware of the fact that a major part of the game is inaccessible they can ask for a refund. GOG doesn't hide the fact that some of the content is locked unless and until you connect to IOI. What they do not explicitly mention is what else besides user generated online content isn't accessible and what it means. That's why a lawsuit or class action wouldn't even get admitted. At least not as long as there are other options available to customers and the individual isn't harmed, which isn't the case.
This is why I think arbitration by Ombudsman or consumer legal rights groups is the best thing to do in this case. Maybe GOG will have a change of heart or maybe they are asked or ordered to decouple all games from their client, so we finally get to enjoy the full content, items and whatever else we paid for. The best possible outcome and in a sense something both GOG and we are going to benefit from.
If you'd ask me, the only thing that can and should be tied to the client, that's achievements. Many players love them and they can or must use the client for that, for social interaction, monitoring of time played, so on so forth. Then they can shop, organize their libraries, keep their content updated automatically. That's the only benefits and the only functions the GOG Galaxy client should provide. It should not act as a gatekeeper to content they did not produce.
Gwent and other CDPR games being the exception. This is what it is about for me and why I will write to both this country's Ombudsman as well as the EU one come Monday.
Let's hope for the best. :)