Hi Erik,
Sorry for the delay. To answer your question, GeoServer with the plugin for GeoGig should run on any 64-bit system that has a 64-bit Java 8 JVM and is supported by RocksDB. This includes Windows, OSX/MacOS and various Linux Distributions. However, the development team is fairly small and we don't have the resources to test on everything included in that general list.
As far as Windows goes, I don't know if GeoServer/GeoGig has been specifically tested on any Windows Server versions. It's been tested on Windows 7, Windows 8 and Windows 10, but most of that testing has been ad-hoc, and usually only happens when an issue related to Windows is reported. It's not currently something that is done with regularity.
That said, I still find it strange that you are seeing the ClassNotFound issue on Windows Server 2008. I am not aware of anything specific to the Windows Server series that would prevent GeoGig from running as expected. I would expect it to run on Windows Server 2012 as well, but again, I have not personally tested that OS. I'm going to try to see about getting a Windows Server 2008/2012 machine to test against and see if there is something about that OS that is different than the Windows 7 OS I have been able to test against.