He said that the current third doesn't attach to anything anyways so it's not a big deal?
The C14 inlet has a ground terminal that can be attached to the chassis. Assuming it's not a dummy wire then if that is properly screwed to the metal case then the chassis should be grounded.
But it does not directly ground the AC-DC unit itself, if the unit is screwed to the case then it'd be grounded to the case, or through the motherboard if the mobo is grounded via the standoffs.