Has anyone had success running a Windows-based GOG game inside of a virtual machine (e.g, VMware VM running Windows 7)? If so, did you have to make any tweaks to make it work?

I did that several years ago for a couple games, I guess it was with qemu but since it was a long time ago I might be misremembering, so maybe I used something else like VirtualBox instead.

On the other hand I have not had any need for that lately, WINE already fits most of my needs for playing Windows video games.

I'd probably suggest looking at PCem

No need. Wine does just fine.

And you had better keep those airgapped.

Depends on the game really. Older games? Sure. But if it uses modern graphic functions, it most likely won't work in a VM. Then you need something like the already mentioned Wine.