Dominion Wars works fine on my laptop - a MSI U210L, which has ATI x1250 IGP and Windows 7 x64 SP1. I think this game only works on specific range of old video cards.
ATI 7500~X1000 series
nVidia TNT2~GeForce4 series
I had it worked on WinXP and Vista before, so the video card is the only problem that decides if it plays normally.
Check my youtube channel for some Dominion Wars videos, recorded from WinXP and Win7.