Installing Linux on a Chromebook is easy. How to Geek has a great install guide for linux and crouton. This guide has a couple of options, I suggest xfce as a solid OS for your Chromebook. I mention this because I am using Ubuntu and Unity, which is less optimal. This instructions will work for many types of linux, so use whatever your heart desires.
Once you have linux install go ahead and use chrosh to open it up. Your commands are: "shell" and "sudo startunity", if you have Ubuntu Unity or "sudo startxfce4" for xfce. If you have another flavor, your sudo start command will be different.
If you are using Ubuntu, sometimes the Software Center is broken when first launched. Update it by typing into the terminal: "sudo apt-get update software-center". Once this step is complete, open it and install WineTricks. This will install a basic Internet Explorer. You can reach that directory by going to: home/chrome/.wine/dosdevices/program files (x86)/ or simply searching for iexplore.exe.
For some reason, the iexplorer.exe will not download the file, but keep it open in the background for later. Open your linux web browser and go to www.play.net/software/.
Next download the Game Entry Client. This will get a program called sg32inst.exe.
Back up in the browser and do the same for the Game Launcher. This file is called InchInst.exe.
(If you have any problems, let me know in the comments and I will try to work it out.)