That's strange. You should have received two pieces similar to the one on the right, accept there will be a left and right side pieces to match the contour of the bumper. there should also be a black metal bracket that attaches to the plastic pieces in your photo, and that the license plate attaches to.
But to tell you the truth the whole mounting assembly will probably get knocked off by the first person that "taps" your bumper in a parking lot. After mine loosened up and wouldn't stay on, I ditched it and mounted the plate directly to the bumper. I had to drill new holes in the plate to line up with the holes already in the bumper, but now the plate sits about and inch lower and almost flush the the bumper.