I picked up some useful information in another forum about how the game doesn't work with CPUs with more than 4 cores if you have Windows 10 or 11. Rather than their idea, here's a simple way to get the game to run on Windows 11 without adjusting the number of cores on your system across the board.

Open the "Launch Dead State" shortcut that is installed. Pick Properties, then Shortcut. In the target, put the following text in the field. C:\Windows\System32\cmd.exe /c start "C:\GOG\Dead State\ZRPG.exe" /affinity F

This assumes you've installed it in the C:\GOG directory

It pops up a dos style window, when it does type ZRPG.exe and hit enter. And that's it.

There's probably a more elegant way to not have to type in the dos style window, but I'm thrilled the game now works.
Support, you may want to sticky this or update your shortcut that gets installed.