Good thing you are using Steam
Go to your SteamApps folder and Deus Ex Human Revolution should have a folder in "common"
/home/james/.PlayOnLinux/wineprefix/deusex/drive_c/program files/steam/steamapps/common
Of course put your login and correct virtual drive name in the path.
I was just guessing.
Now drag-n-drop it to your desktop
Then remove the entire virtual drive
Re-Install Steam and then drag-n-drop the game folder back into "common"
Click "install" in Steam and after a few menu's it will start "discovering files"
Then it will say "Finished"
You can do this over and over without having to re-download the entire game.
Before I address the errors and bugs, a few questions:
What distro/version are you running?
Is it 64-bit?
did you install the 32-bit libraries?
What video chip are you using? AMD, GeForce?
What libraries are already installed to run Deus Ex HR?
Looks like it will require:
d3dx9
vcrun2005
vcrun2008
vcrun2010
Newer versions of Wine (1.6, 1.7) have a checkbox under Display Tab about “automatically capture mouse" in virtual desktop.
So make sure you are using virtual desktop and then check that mouse capture.
That should fix the mouse problems.