I have the original retail version of Gothic 2 but it does not work at all, the process does not even appear in task manager when i try to execute it. Sometimes the process starts but then I am greeted by the Gothic 2's DRM saying I have virtual disk drives when I don't.

Now i wanted to know if the game will actually start if I buy the gog.com version of the game, Or is the gog.com version of the game just the retail version up for download minus the DRM?

I'm under the impression that the GOG version has been tweaked a bit to make it run well on modern systems. I played it on WinXP (32-bit) without any issues to speak of, and as far as I've seen from the comments most people are able to run it just fine on Vista and Win7 systems as well (there are still occasional issues reported, but nothing particularly systematic). There was a known issue on systems running 64-bit Vista or Win7 and using Nvidia cards, but it seems the most recent Nvidia drivers sorted this issue out.