Is that an Anthony-Sylvan by any chance? Your setup is very similar to mine. Yes, the pool drain return lets water go back through the floor drain. They suggest it warms the water faster. I am not totally convinced it does but it might--I do use it in the Spring and surface temp does go down; therefore it must have some effect. I also like it for vacuuming because it does not disturb the surface and helps get crud out from around the pool drain.
The important thing is to never open Pool Drain on the suction side and Pool Drain Return on the return side both at the same time. You will then create a short circuit loop and you will just be recirculating water that never leaves the equipment pad. The Pool Drain Return does make blowing out the lines in the fall more complex, but I have it down.
If it is A-S, at least they didn't give you a Nature2--I hate those things.
EDIT: If you want both your skimmers to work full blast, turn the leftmost (topmost) valve in the first pic so the handle points to the right in the same direction as the horizontal pipe. That valve is to adjust between the two skimmers; as set, one of them is at half force or less.