According to Bill :
I'm not quite sure what you are talking about. Is there basically an
extension cord which terminates with a 3 gang box and this 3 gang box has 3
regular duplex electrical outlets (3 prong), and the plug on the extension
cord is 3 prong, and you have looked inside the 3 gang box and are wondering
if it is wired correctly so far as the grounding goes?

I believe it's an in-wall triple box.

I personally wouldn't do it that way. I use an ordinary box/outlet on the
wall, and mount a power bar (or even two) on the back of the entertainment
center. This is how it's commercially done, ie: racks of computers.

Anyway the proper way to wire the grounding wires to a 3 gang box with 3
outlets would be to have a separate grounding wire or "pig tail" going to
each outlet grounding screw, then use a wire nut or crimp connector to
connect the 3 grounding wires with the ground wire on the power cable. Also
to have a 5th wire screwed to the 3 gang box if it is metal.

Bob's suggestion is best:

Cut the ground wire really long. Loop it under the box's ground screw
first, then continue to the first, 2nd, and third device, making a more
than 180 degree loop under each ground screw. The secret is to not cut
the ground wire.

When you do things this way, it takes up remarkably little room. The only
change I make to his suggestion, is to have the ground wire loop around
a screw on _each_ box, and then to the outlets. You can have as many
outlets as you want, and you only need one wirenut, one continuous wire.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.