C,
There is no way for us to tell for sure...
Normally when you have two skimmers there are two valves, one for control of each skimmer, at the equipment pad... To have only one valve does not give very much control over which skimmer gets the most suction.. It would also mean that your "useless" main drains are connected into the bottom of at least one of the skimmers, as it does not go back to the equipment pad.
That said, it depends on the plumber.. It could be that your plumber connected both skimmers in series so that one pipe is for the skimmers and the other pipe is for the main drain.. (There is only one main drain, even if you have two drain covers)
They are useless because your pool will work just fine without them.. Operationally, you can't tell the difference between pools that have main drains and those that do not..
Only you will be able to tell for sure..
Turn the valve handle to point up or down and then go feel the suction in each skimmer.. With the basket out, and right at the pipe in the bottom of the skimmers..
If both skimmer have suction then you will know the valve has nothing to do the the skimmers.. If one of the skimmers has suction and the other does not.. Go turn the valve so the handle is horizontal, like in your pic, and make sure the missing suction comes back..
You can also tell us what you see under the skimmer baskets.. Do you have a floating diverter valve?? Do you have one open pipe or two open pipes?.. The pipe nearest to the water is normally plumbed to the main drain if it is not plugged..
Let us know what you find out...
Thanks,
Jim R.