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To everyone who can't run this game and still has issues... for ages now I had the same problem, the game wouldn't start for me, immedietly crash on boot. I tried everything and almost nothing worked...
However, there is a file in your main folder that gives you a hint what's the problem with your current instalment. It's called Sherman.txt - if game works fine, it should be empty, if it crashes, it should have a brief summary of what screwed up during launch.
To my surprise, and possibly to your's aswell, it's a problem with Voice Recognition - yes, as silly as it sounds, Rainbow Six the original game tries to force voice recognition in your game. Seems like everyone just forgot this feature even exists. Now, to run this game without installing some dated voice recognition support for Windows, and I bet if you have this issue you won't have it in your system, here is a quick walkaround that worked for me!

Here is how you fix it!
1) Remove Rainbow Six from your HDD completely. Just uninstall if you have it installed, then delete whatever folder might remain in GoG Galaxy/Games/ - if there still is Tom Clancys Rainbow Six folder - delete it!
2) Download VLC codeck pack... for some reason it works.
3) Make sure RainbowSix.exe (in your main game folder) is set to compatibility mode with Windows 98 and runs with Administrator Rights.
4) Find an executable in same folder called "DevicePicker.exe" - in properties set it to work in compatibility mode with Win 98 and use Administrator Rights. Now run it.
5) There check the option "Forbid Voice Recording"... you can also set the Render method to Software Render while at it... and click OK.
6) Run the game.

It should work now, it certainly worked for me. Cheers.
Post edited May 14, 2018 by YuriPRIME
Doesn't work.
Using dgVoodoo fixed the startup problem.
This is utterly unacceptable by GoG to sell broke ass shit like this.