Executing from the menu item, nothing happens.

Executing from console, I see this:
r@r-PC ~/GOG Games/Wasteland 2 Directors Cut $ ./start.sh
Running Wasteland 2: Director's Cut
Set current directory to /home/r/GOG Games/Wasteland 2 Directors Cut/game
Found path: /home/r/GOG Games/Wasteland 2 Directors Cut/game/WL2
Mono path[0] = '/home/r/GOG Games/Wasteland 2 Directors Cut/game/WL2_Data/Managed'
Mono path[1] = '/home/r/GOG Games/Wasteland 2 Directors Cut/game/WL2_Data/Mono'
Mono config path = '/home/r/GOG Games/Wasteland 2 Directors Cut/game/WL2_Data/Mono/etc'
displaymanager : xrandr version warning. 1.5
client has 4 screens
displaymanager screen (0)(DVI-D-0): 1920 x 1080
Using libudev for joystick management

Importing game controller configs

....... Then nothing happens.

Any ideas on how to get this running please?

Have you tried 'ulimit -n 4096' before running the game or adding to start.sh?

I feel like I'm repeating myself, to no avail. Can gog just finally fix it (lord knows inXile never will)? That way, when somebody posts something like this, I can just shut up and ignore it, since I have nothing useful to add.

Initially there was some other problem. I read about people using what you mention to fix it, but my fault wasn't that. After playing around restarting, I finally got it to show the loading/menu screen (I don't know what the first problem was stopping it getting here at first though).
Then, I got further in and it quit out upon starting a new game - this is where I read that the fix you mention is required. I added it to the startup script, and now it runs fine.

Yeah it's crazy why they don't just add that line to the script!? Maybe they WANT people to have problems? Haha

OK, well, like I said, I have nothing further to add. Try reading the player.log file (~/.config/unity3d/inXile Entertainment/Wasteland 2: Director's Cut/Player.log). Try running WL2 directly (i.e., without start.sh's addition of LD_LIBRARY_PATH elements). Try running the game with strace (that's how I found out about the massive number of leaked file descriptors that the ulimit command fixes): strace -fo /tmp/st.log WL2. Basically, the usual procedures.

It Works!
Thank you Kind Sir, may God Bless you with a bunch of kids.