Found the problem. I knew my system had McAfee AV installed, and so had it disabled during the install. However, my system also had McAfee's Host Intrusion Prevention Services (HIPS) installed. HIPS was blocking the changes to the registry from the VMware Workstation install.
I hadn't noticed the icon for HIPS when logged on as my accont. But, when logged on as the local administrator I did see it. Then checked its log and found all the related errors and warnings.
So, disabled HIPS and the install and license registration completed successfully.