Galaxy can be required for multiplayer aspects in games, but if what you say is true for the singleplayer part of the game, GOG will consider it a bug, and will get it fixed.
There's nothing in the Crime Cities GOG forum about this, nor in the various tracking threads in the main forum, and generally GOG users are extremely sensitive about anything which even reeks of forcing Galaxy, so I'd strongly expect any issue to be known.
I've seen cases where the developer implemented a bad online check, so that if you blocked the program from accessing the internet while the OS reported being online, the game would hang or crash, but being fully offline would work. Could it be that something like that was at play here? Oh, or that you simply picked the wrong installer for the game, and thus ran the Galaxy-installer rather than the offline installer?