I added following lines to Conquests.ini to make the game to start:
PlayIntro=0
KeepRes=1
There is a new workaround to black terrain bug in the link:
https://bugs.winehq.org/show_bug.cgi?id=41930
Rename /usr/lib/i386-linux-gnu/libOSMesa.so.8 to something else so that Wine won't use it.
After those fixes, the game can be played, but there are audio issues (as described by other users).
I installed from iso, not from Steam.