I have purchased and download Tyranny (Archon) through GalaxyClient. The game loads to the point where I can select "New Game". After I do, the video becomes scrambled and frozen, the mouse cursor disappears, and the game becomes "Non-responsive." I have a late 2012, 27" iMac with 32Gb memory running macOS version 10.12.1. My video card is NVIDIA GeForce GTX 660M 512MB.
If anyone can help, I'd truly appreciate it because I am about to ask for my money back for GOG.

Support doesn't read the forum. You need to contact them through the support form to file a support ticket. Then they'll be able to help you.

Are you sure your 660M only has 512MB? I just looked it up the the specs say it should have 1GB.

If you are right you may be out of luck since the minimum specs for the game say you need a GPU with at least 1GB of video memory. Then support would not be able to help you and a refund would also only be goodwill.

Looks like video memory is too low. I suggest reducing resolution to something much smaller to help reduce the amount of video memory needed.

MINIMUM:
OS: OSX 10.10
Processor: Intel Core i5 @ 2.9 GHz
Memory: 6 GB RAM
Graphics: Radeon HD 6950m with 1GB VRAM
Storage: 15 GB available space