Currently Wine does not properly support DX11, which this game requires. However, they are working on getting DX11 to work in Wine. It is not easy to say how long it will take, but as with all open source projects, don't expect things to happen quickly.
Cronyk, if you like Warhammer 40k, be sure to check out Dawn of War 2, it has a native Linux version that runs great. There is also another game on Steam called Space Hulk Ascension (as well as the original Space Hulk) which is a turn based game based on the board game of the same name. These games also have excellent Linux versions.
As for Deathwing, it was made by Streum on Studio, same people who made E.Y.E. Divine Cybermancy. They have no past experience in supporting Linux so I would not have too high hopes for a Linux version for this game. Personally I'll be checking Winehq to see if anyone has reported luck with this game before I try it myself.