I have not been able to install yet. Lucky for me, I also have the Steam version. If anybody has found a way to get ADOM up and running, please share how you were able to find success.

Many thanks, and good luck to all you ADOM devs with the new launch!

Edit: I was able to run ADOM by installing libidn-133-compat and lib32-libidn-133-compat from the AUR, and then creating symlinks from libjbig2dec.so.0 to libjbig.so.0 in the /usr/lib/ folder. In addition I needed to create a symlink from /usr/lib/libtiff.so.5 to the game/lib64/libtiff.so.5 file in the ADOM folder.

Good to know. All works well so far. I love the music, and the new popup messages that appear. I never knew how quickly one becomes corrupted in CoC!

The game works also on Devuan (it's a Debian without systemd). The game complained about missing SSL libs and this is because the libcurl that comes with the game is linked against older versions. The game started working after I simply removed the libcurl.so.4 from game's directory so it could use the one in my system. I tested the creation of a game account so it seems networking works. I assume that libcurl is used for that.

Shame on GOG for claiming support for Ubuntu is paramount to provide a Linux version ...

If you want to run ADOM 3.3 on Debian 9 (Stretch) you have to delete libcurl.so.4 from the game folder, and if it is not already on your machine, install libcurl3 with: sudo apt-get install libcurl3.

Well, installing wasn't the issue, getting it to run was.
Thanks to your hint I got it running by:

$ ln -s /usr/lib/libjbig2dec.so.0 game/lib64/libjbig.so.0

and

$ mv libtiff.so.5 libtiff.so.5_bkp

in the game/lib64 directory.
Sorry for the excessive spacing, you know how horrible formatting text on GOG is.

I finnaly gathered all required libraries to run ADOM. You can find them here: cloud.disroot.org/s/5bawGskKfHZtkPo

Also you need this:

LD_LIBRARY_PATH=./lib64/ ./adom64