I do think your dice are from Chicago, but there isn't really much to back up the attribution. I have found quite a few of them in the Chicago area over the years (including once a glass rolling pin stuffed full of them), and they're typical "Chicago style" dice. I've never been able to find any mentions of the West Side Club in the Chicago newspapers from the era. They're not rare as fair dice, but if loaded then I think that would make them pretty scarce.