Even simple motor, apparently not requiring any loop but a piece of the wire is shown on the photo below.
 Elements of  the set:
1. Neodymium magnet.
2. Iron nail
3. Volta pile  R6 (1,5 V).
4. Piece of wire (see photo 1)  
 
Understanding the principle of operation of the engine 6b, it is easy to explain the present one. This is just Newton’s principle of action and interaction. Essentially, this is the piece of wire (forming the loop) which should spin around the magnet as in the previous case. But now the loop is hold fixed, so by the principle of reaction the magnet spins in the opposite direction, instead.
 
Note that the engine moves with the highest speed when the wire touches the magnet in the middle of its heights: the magnetic flux closed by such a loop is maximum. When the wire touches the magnet below than the total flux is smaller and the turning around is slower.

Photo below: The engine with one-loop: the battery, nail, magnet and the wire. The wire should touch the magnet at half of the height to assure the highest speed of turning.