What worked for me:

1. Download game from gog.com without galaxy installer, so just download separate parts, part 1 and part 2.
2. Download wine and winetricks

sudo apt install wine64
sudo apt install winetricks
winetricks d3dx9
winetricks vcrun2005
winetricks vcrun2010

3. Install the game from setup_anno........ exe

4. Run game and you will see black screen.
To overcome this, find file Engine.ini located in
/home/<your_username>/.wine/drive_c/users/<your_username>/Application Data/Ubisoft/Anno1404/Config/

Edit following line:
<DirectXVersion>0</DirectXVersion>

And set it to
<DirectXVersion>9</DirectXVersion>

5. Save the file, run the game.

Hope that helps someone in future! P.S i'm not running Ubuntu on Wayland but on Xorg ( not sure if that will change or impact anything but just mentioning that as a side note ).

Good luck!

Works without any winetricks for me. Needs to be configured to use DX9 as described above. 64 bit prefix, and I also applied the 4 GB patch to both executables; not sure if that was necessary, but it may improve stability.