Leucius: I just installed Gothic earlier on a Windows 10 build, and it started up with no issue. I know this doesn't exactly help you, but if you have updates deferred, you might want to install them.
I am using the most current build of Win 10 (CU)
WildHobgoblin: Just since you already posted here - so you downloaded it recently from Gog, and the game worked out of the box?
I'm asking since I still have a physical copy lying around, which, with much pain, fiddling, and downloading of patches I got to work on my old Win 7 PC.
I'm kind of tempted to repurchase the game on Gog (since it's very cheap right now), but really only if there aren't major hiccups to be expected, since I already went through that once ;) I'm on Win 10/64 bit, same as the OP.
Sorry about the delayed response, I was at work earlier, and then played through The Vanishing of Ethan Carter. Yes, I bought Gothic 1 a day or two ago when it first went on sale, installed it, and fired it up using Win 10 with no tweaking needed. It's 100% vanilla, as vanilla as the GOG version is, anyway.
I am greatly annoyed when GOG versions require tweaking to get to work properly, but that isn't the case with this one. I'm planning on starting my "official" playthrough very soon :)