I think the idea here is to introduce flow that is contrary to the expected vortex direction hence the cut out's shape. As there is a low pressure area behind the wing between the endplates, the the flow will want to vortex one direction behind the flap and the other direction rolling off the ednplate. The shape of the cut out will determine how that forms.
I'm guessing that the sum of the drag from the two vortices formed this way is less than the drag from one big vortex and so is considered preferential.
Don't forget that the louvres in front of the flap in the endplate will allow some high pressure bleed outwards which will reduce the pressure differential at the end of the flap. This will also reduce the resultant vortex and so improve efficiency.
That's how I see it anyway, for what it's worth.