How do you close a VMWare Fusion VM Window without shutting it down or suspending it?

There is a better way (at least with Fusion 8)

VMware Fusion > Preferences and tick the "Confirm before closing" checkbox.

Now, when you close a GUI window, you will receive a prompt with buttons for Poweroff, Suspend, etc... You will also see a button to "Run in Background" which will close the GUI window but, leave the VM running in the background.

I haven't tried it yet, but it seems like this answer on AskDifferent might be what you're looking for:

An additional way, you can start up the VMs you want and then force quit VMware Fusion using Command+Option+Shift+Esc

The GUI quits but the VMs run in the background. To manage these VMs you can start VMware fusion again as usual and it will show you what's currently running.