I have Steam installed via Wine 1.6-rc4 and installed Dishonored in Steam. I checked WineHQ Appdb and it says Dishonored is gold in Wine, so I thought it would be a good place to start and test it before I go to other games.
The problem is if I launch the game either from the
dishonored.exe or from the Steam game page, it first loads with
installing direct x11 (first time setup), then loads a black screen on my left monitor, and then returns to desktop (the desktop resolution drops to 1600X900 from my 1920x1080 and the mouse is unresponsive till I open up the terminal). The game is still running in the background and I need to force quitting Steam.
I have Radeon 7970. I have EVE online installed and working just fine on its own, no problems. (It's not Steam EVE).