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Ancient-Red-Dragon: If by "to run" you mean "to run the game with missing content," then you can indeed run the game with missing content without using Galaxy.
Gersen: You have a bunch of t-shirts and one weapon that needs to be claimed using Galaxy.
Thanks for the replies!

This apparent tactic of using pieces of a game---either withheld or "purpose-built"---in order to encourage certain behavior should not itself be encouraged in my opinion. But I am relieved to find that the game does not require a Web-based account as I had rightly assumed.
Time4Tea: Content is content. Why should we give GOG a free pass at the thin end of the wedge? Just to watch them push the wedge in further?
I just answered Dryspace question, now it's up to him (or her) to decide if it is a deal breaker or not.
paladin181: I agree with ponczo. The difference is I don't think such games should be on a service that advertises itself as DRM free. Publishers and developers can use any means of protection they choose. But here it should be none.
Time4Tea: Sure, developers should be free to design their games how they choose. But they shouldn't necessarily be free to sell them on here, on a store that markets itself as 'DRM-free'.
Exactly what I said: "Here it should be none" as in here on GOG it should be no DRM.