Select the virtual machine in the library listing and press the delete key.
How do I remove (delete) a client from the my VM Library list?
You could read the documentation... Have a look at: VMware Fusion menu > Help > VMware Fusion Help > Using the VMware Fusion Interface > Using the Virtual Machine Library Window > To remove a virtual machine from the Virtual Machine Library window >
Actually, I did go to VMWare Fusion Help and typed in "remove" and got:
Configuring the Sound Adapter
Adding a Floppy Drive
Adding and Configuring a Parallel Port
Adding and Configuring a Serial Port
Configuring the CD/DVD Drive
Configuring the Network Connection
Sharing Files Between Virtual Machines and Your Mac
Using the Virtual Machine Library Window
Since I was looking for the word client, it did not occur to me to open up that last item. I suppose that if I had opened that one, I might have found the answer that you provide.
Since I was looking for the word client
FYI, "client" is not a word we use to describe virtual machines, so looking for it will give poor results. A "guest" describes the operating system running in a virtual machine, but from your question, you want to delete the entire virtual machine, not just the guest.