Welcome to the Community,
did you select ESXi as the guest OS in the New Virtual Machine wizard. The virtual NIC model that's used/created for the virtual machine depends on the OS selection. Open the VM's configuration (.vmx) file to see what NIC type was created and add ethernet0.virtualDev = "e1000" if it doesn't exist. If you are going to manually edit the .vmx file make sure the VM's tab in VMware Workstation is closed, so that the configuration file is re-read after you are done with editing.
Man you are great, so far this looks like it is working. I confirmed that I did select ESX as the guest operating system and for some reason it is not making : ethernet0.virtualDev = "e1000" in the config file. Not really sure what the root cause is but at least your work around works.