This is not a fix that I might have found. Just noting a couple of things.
( Note that most, if not all other of my games on GOG, even as old as Tomb Raider 3, work decently.)

I did a lot of looking around on why it was crashing almost right off the bat.
Can't believe all the articles about this issue.
The game worked fine when I first got it a year or two ago.
I did replace the old but pretty good MSI Geforce GTX 980 with a new EVGA GTX 1080Ti card (very good one)
Bad news: I can't finish the game for now.
And, it will not play on STEAM Win7 or GOG Win10.
Good news: I only downloaded the free GOG version.

I might try it with the MSI GTX 980 but not anytime soon. It did work very well with that card.
Still, the bulk of the games I have on STEAM and GOG work fine with the 1080Ti. Go figure.
And yes, I did not play around with OC on the new video card. Maybe later.

Maybe try an older nVidia driver before you go ahead and swap out your gfx card.

The game works for me using nVidia driver 416.94 atm (haven't bothered updating in a while). I also have a GTX 1080 Ti, using Windows 7 Ultimate, 64-bit.

I will try that out. Thanks!

190604:

Did not work. Keep getting errors that there seems to be a problem between URE4 and D3D.
Web searching shows many possible PC specific issues that could cause that.
Another issue came up once or twice as well but did not log that one in while focusing on this one
Set this issue aside for now. Will put in a support request later because I can't figure it out.