Thank you for your reply but most of that went over my head. Just to clarify, are you saying the resistance between the 2 points marked in red should read zero ohms and I should go ahead and connect them?The center pin is ground, most certainly needs to be connected, and probably is connected. The center pin is connected to the heat sink surface on the top of the chip that appears to be soldered. If in doubt, check it with an ohmmeter. That short pin is likely zero ohms to the pad it isn't soldered to.
Or is the short leg just an extension of the long piece across the top of the chip which is soldered to the board?
The 78M05 chip is listed both with and without the centre leg: