I could install, launch the game fine enough, but... the "action" hot-key just does not work, whether at original controls, or after remapping. :( :(

Curiously, I could remap the movements to W,A,D,S but specifically the actionn key just did not work, and not being able to pick up any weapons, equipment, so on and so forth, is really a game breaker.

Has anyone had similar issues with Windows 7 - and are there any remedies?

This issue seems just erratic, which is rather frustrating...

That's Gothic 1's bizarre control implementation. The action key has to be used in combination with a direction, so action + forwards attacks or talks to people, action + left/right moves items around in chests and when trading, etc. Hitting the action key on its own does nothing.

You can change the bindings to whatever you want but you'll still have to use them in combination like this to actually do things.

Gothic 1 (from GOG) is supported by the latest PlayOnLinux install. I have it on an old AMD machine running Debian. Seems OK, except stuck in a window. It wouldn't be so bad, but there are no in-game resolution selections that make the window anywhere near full screen so it's wasting a fair amount of screen real-estate.

It's a little unstable. I've had a couple of random crashes for no reason and glitches where the character just dies; i.e. standing next to a pot of water and somehow he magically warps into the pot and drowns. No way to get out of it. I recommend saving fairly often to avoid it.

I played gothic 1 back in the day on wine, was able to finish the game but I must note it had its points where I wanted to burn down my tower .-. ... anyway, a easier way of doing this is install windows 2k on a vm and then just use task man to close explorer and all other running processes and you get almost all your computers specs, I've done this once before just to test it, gothic 3 ran beautifully after a few configs and mods to get it working on 2k :b. This coming from a dual booter with linux as my main OS and winxp as my gaming OS :)

It works pretty well in both Arch Linux and Ubuntu. I do have occasional crashes on load where the game seems unable to find a sound files, so rotate savegames, which is a good idea for these games anyway. I don't know whether the systempack helps any, I couldn't install it for some reason (install button was greyed out after selecting the game directory).

Just installed through POL and added directmusic. On Ubuntu I use WINE-Staging from winehq. On Arch I just use the latest regular WINE.

I've installed it with wine directly (so not through PlayOnLinux) and game crashed right before reaching the main menu.
To fix that you need to install directmusic (as done in POL and pointed by @hollunder) with:
winetricks directmusic

That allowed me to go past the starting menu.
But then the game had messed up texture. I checked WineHQ for help and in one note they tell about the use of "S3 Texture Compression (S3TC)" by this game which seems to be an issue with open source graphics stack.
The suggested driconf fix didn't work for me, but I managed to find a package solving the issue : libtxc-dxtn-s2tc (Texture compression library for Mesa: S2TC is a patent-free S3TC compatible implementation and provides texture compression to Mesa.)
sudo apt install libtxc-dxtn-s2tc

Finally I adjusted the settings in Gothic/system/GOTHIC.INI:
zVidResFullscreenX=1280
zVidResFullscreenY=1024
zVidResFullscreenBPP=32