It works perfectly for me. The only other thing that may have an effect on my system is that I usually use wine-nine, in the form of gallium-nine-standalone
on gentoo. Maybe you could try the full "winetricks d3dx9" suite. IN any case, I found the issue to be massive shader compile failures.
edit: I suppose I should also mention that I use wine 4 stable (currently 4.0.3). I think wine-nine is incompatible with wine-5. I could try without wine-nine and with different wine later today, but I won't reply about it until ljate tomorrow at earliest.
edit 2: works perfectly without wine-nine, in both wine-4.0.3 and wine-5.0.2, as long as you have the native d3dx9_43. I haven't tried it without d3dx9_43, and won't. The only other fix I've ever applied was d3dx9_30, which was necessary with an older version of Fantasy Wars, but I'm sure you're using the latest from gog, so that wouldn't do anything.
It's probably your video drivers. I'm using recent Mesa with Radeon, as I've been doing in various forms as long as I've owned Fantasy Wars.