The clamps are designed with a long and a short side, but in fact only one side is used for any particular wheel. The difference is the long side for the 5 1/2" rims with 7.50 16 tyres and the short side for 5" rims with 6.00 16 tyres.
On the Army SIII the bolt goes in from the short side so that the long leg touches the top of the round bonnet bracket and the bolt screws into it.
With the wheel on the bonnet, the clamp is turned so that one leg sits on the round bracket and the other end is resting on the wheel centre and then the bolts are tightened up.
To remove the wheel. You will note a curved side and a straight side on the "dogs leg" clamp as you described it. The clamps are rotated so that the curved sides align with the curve of the hole in the wheel centre and the wheel will lift up.