Earth Grounding an HV Power Supply
Consider this scenario: While the power supply is turned on and outputting a high voltage, somebody abruptly removes the power cord. 

This would break the "protective bonding" provided through the power cord. However, capacitors inside the supply, or in whatever its output is connected to, could still hold a high voltage. It could take seconds or longer for such capacitors to discharge. If there is a leakage path from the high voltage to the case, the case could become hazardous during this time.

Having a second earth connection reduces the risk in this scenario.

I don't know which safety standard this supply is designed to, but I have access to IEC 61010, which is the safety standard for many kinds of test and measurement equipment, and other safety standards tend to have similar requirements. In section 6.5.2.2, 61010 requires,


  Equipment using PROTECTIVE BONDING shall be provided with a TERMINAL that is suitable for connection to a protective conductor and meets the requirements of 6.5.2.3.


And in section 6.5.2.3, 


  b) The integral protective conductor connection of an appliance inlet shall be regarded as the PROTECTIVE CONDUCTOR TERMINAL.
  
  c) For equipment provided with a rewirable flexible cord and for PERMANENTLY CONNECTED EQUIPMENT, the PROTECTIVE CONDUCTOR TERMINAL shall be located near the MAINS supply TERMINALS.


I'm not certain, but this distinction between an "integral" and a "rewirable" protective conductor or flexible cord may be why a device using a removable power cord might be required to have a separate protective conductor terminal.