Before you do anything else... do you have the video drivers installed?
AMD or Nvidia
Make sure you have the correct Windows Packages installed. When you install Steam just the basic libraries are installed, but doesn't mean games will run. You still need to install DirectX, Visual C, Physx, etc.
It really depends on the game.
What version of Wine are you using?
What distro are you using?
If you are using 64-bit Linux, then 32-bit libraries have to be installed to play games.
I know it seems like a lot when this stuff works out-of-the-box in Windows, but we can help you get it started.
I have a guide for Dead Space, but its the retail version not steam:
Dead Space