This is the tricky step. Unlike VMware Server, the Infrastructure Client does not have the File > Open option, allowing you to browse for existing .vmx configuration files and registering them. So it seems you might be stuck.

The answer lies in the datastore. In the destination folder, where you have just created your clone, right-click on the .vmx configuration file. Select Add to Inventory.

via How to clone virtual machines in VMware ESXi.

Update:  This indeed worked.  The problem occurs in that if a .vmx file is copied directly from Workstation, it can contain erroneous info that can cause problems.  In my case eth0 would not pass traffic.  I noticed something wrong by examining the virtual machines on Configuration -> Networking when the esxi box is selected.  I noticed the vm I was having problems with wasn’t listed so I thought to examine the .vmx file.

The copied over .vmx file had ethernet0.vnet=”/dev/vmnet0″ which is a Workstation reference that doesn’t apply to esxi.  By eliminating this and adding ethernet0.networkName = “VM Network” networking worked.