How do I properly earth this voltage regulator that only has a two-prong plug?
The nicest way would be to open up the unit, remove the 2-core wire currently fitted, and re-wire it with a 3-core wire and a 3-pin plug,  Connect the ground wire to a suitable screw inside the chassis.
A simpler and less elegant way would be to remove the 2-pin plug, and replace it with a 3-pin plug.  Run a separate ground wire to the terminal you have identified.
But check whether or not the manufacturer has bothered to connect up the ground terminals on the output sockets.  If not, they need to be connected as well.