This process will get you a virtual machine running Ubuntu Linux 14.04 LTS 64-bit, with enough OpenGL support that Steam will correctly install and run games built in Unity. It won't necessarily run them fast, but they will run.
- Download and install Oracle's VirtualBox. At the time of this writing, I used version 5.0.2 on my Windows 7 machine and test build 5.0.3-102290 on my Windows 10 machine.
- Create a new virtual machine. It should be set for Linux, Ubuntu 64-bit, and the following:
- 16Gb virtual hard drive (or more)
- 2Gb RAM (maybe more, maybe less, but this is ideal)
- 128Mb video memory (the max VirtualBox supports)
- 3D acceleration checked
- Make sure to reboot after this installation
- Open a command prompt/terminal. Use Ubuntu's "Search your computer" icon at the top of its system bar and enter "terminal".
- Run the following: sudo apt-get install libglapi-mesa libcheese7 libcheese-gtk23 libclutter-gst-2.0-0 libcogl15 libclutter-gtk-1.0-0 libclutter-1.0-0 xserver-xorg-input-all
- The Steam package downloaded from the site will install an actual Steam installer.
- Running that installer will prompt a terminal window to install further OpenGL dependencies.
- After all of that is installed, the normal Steam client will install and update
At this point, Steam should be ready to log in, and you can proceed as normal. Log in to your account, install the games you wish, and test.