I've been playing The Ground Gives Way myself in Linux, using the instructions from the section "Running TGGW on Other Systems" in the game's official FAQ, but apparently that won't work in certain systems with certain versions of Wine. So, since I know it works perfectly with the version of Wine I have on my system (version 2.7, built from unmodified source), I used AppImage to package up the Wine files together with a simple run script into a hassle-free The Ground Gives Way launcher.
This launcher DOES NOT install anything extra to the user's computer (AppImage works by mounting itself as a virtual filesystem overlay, meaning it is sandboxed from all system-wide files), but does create a seperate wine prefix in ~/.wine-appimage so as not to interfere with the default one in any way.
This launcher should work on pretty much any other relatively recent 64-bit (x86_64) GNU/Linux distro, but currently requires multilib support (I plan to eliminate that requirement soon, if possible). To use it, simply place the launcher file into the same directory as The Ground Gives Way.exe and run the launcher file. It does not need to be run from a terminal (as it opens its own xterm window). Also accepts cli parameters to change the xterm launch options (such as giving it a bigger/smaller font, changing the background color, etc), a --console option for running the game in the current terminal rather than opening a new window, and a special --debug option that echoes the entire final command before running it. Requires xterm (unless using the --console option). Tested and working with both the Windows 10/8/7/Vista version of The Ground Gives Way and the XP SP3 one.