Yeah, simple as. Just download (I think latest version is 1.74 or something like that), extract and click. There are a lot of options you can juggle with once it's installed.
You can turn combat modifications on or off, for instance (I recommend on), choose whether to make the game more challenging by revamping the levelling and learning points system, some graphical effect, etc. There are pop-up tooltips for them, though, so it should give you a fair idea once you get to the game menu.
I'm actually a bit jealous! I'd love to be able to play patched Gothic 3 for the first rime again. It's really only rivalled by Morrowind for me in the genre of swords-and-sorcery RPGs.
Edit: Missed you edit about Steam. I don't know about patching the Steam version, tbh. I think most of the fixes were in place by 1.6, but there were a fair few extra fixes and options (including some more combat modifications) in 1.7. Would be worth trying to see if you can patch the Steam version to 1.74 or at least 1.7 if you can find out how.