Shaded-Pole motor, how does it work?
I suspect that your confusion is because you may be more familiar with the construction of Figure 1.



Figure 1. A simple shaded pole motor. Note that this simplified diagram does not show the closed magnetic loop between the top and bottom of the poles (so it would be brutally inefficient as drawn). Source: Slideshare.

In the case of Figure 1 the unshaded coil will follow the magnetising current of the primary coil. The shaded poles will follow a little later with a resulting clockwise rotation.



Figure 2. A better diagram. Source: HPACmag.

The motor you have seems to have a core of the type shown in Figure 3.



Figure 3. A multi-pole shaded-pole motor core. Source: Made-in-China.

I couldn't find any authoritative information on this online but my guess is:


The primary magnetic circuit is in area 1, as usual.
This large shading ring shades about 1/4 of that half of the core. The flux in the green and blue areas will be delayed by the shading.
The second shading ring further delays the flux in this area. The result is, I suspect, better starting torque as the rotating field carries on for longer than in Figure 2.
The core is closed to avoid an assembly step but notice the pinch-off at this point and opposite. This is probably determined to be enough to provide mechanical strength without too much flux leakage.
A straight section with a bobbin on it can easily be dropped into this portion.