Is there a way I could fix this problem, or as the question asks, register the product key via the command-line instead?
In a Terminal use the following command and use your actual serial number in place of the fake one shown.
/usr/lib/vmware/bin/vmware-vmx --new-sn 1A2B3-C4D5E-6F7G8-H9I0J-1K2L3M