Aww man, my computer doesn't support hardware virtualization (I checked). Oh well. :/
You don't need hardware virtualization for WINE, that's why it's called "WINE Is Not Emulator": it's just an implementation of Windows ABI for unix-like systems. WINE emulates Windows system calls, but it does not emulate hardware.
However, you need to make sure you have properly configured hardware-accelerated OpenGL support on your Linux system.