I recently purchased Doom 3 and when I start it up on windows 10 under VMware 11 I can hear the Music bu I get a blank white screen and have to reboot the computer. I tried it on Windows 7 with the same white screen appearing. It is very frustrating! Is there a workaround or can I get a refund? I

Doom 3 should work from GOG without the use of VMware. Just install the exe file on your Win 10.

What made you use VMware?

Whether relevant or not, the fact of the matter still stands: the game should work out of the box from GOG without the use of other software. What if Doom 3 from GOG is already working with such software and accessing it through another app creates errors such as the one encountered by the OP?

Since the link shared is creating confusion and aiding in missing the point, would it be better if I removed said link?

Well they said Windows 10 under VMware, which I take to mean that they might not be running Windows (10 or otherwise) on their hardware directly. Shrug, maybe there's another reason for using VMware.

Either way I feel like the source ports are a better bet if there's no native build.

If you're trying to get it running on Mac or Linux you're probably better off with the original game, not the "BFG Edition" GOG sells. If you own it here I wouldn't feel morally conflicted at all about finding the original version somewhere.