To launch your application into a new Xserver instance you simply need to launch the program as follows (I'll use Desura in my example):
xinit /home/honey/desura/desura %U -- :1
Once you run this your screen will flick once or twice as the new X instance is created and the program is automatically launched within it. This new X will be accessible via the keyboard shortcut ctrl+alt+f8, to get back to your previous X instance simply press ctrl+alt+f7.
Now, one other thing to note is that on some Linux distributions you may be greeted with the following message when you try to run xinit as a normal user:
X: user not authorized to run the X server, aborting.
Don't panic, the fix for this is also simple. In terminal run:
sudo nano /etc/X11/Xwrapper.config
This will open a file for editing - we only need to adjust one line. Make sure somewhere in this file is the line:
Save and close the file and the above xinit file should now work. Happy gaming folks!