How can a magnetic circuit with an airgap have a higher e.m.f in the secondary coil than the same circuit without the air gap?
Notice that the primary magnetic field has two places go. The middle iron, and then the iron under the secondary. 

Any magnetic field in the middle iron is not coupling to the secondary.  

With no air gap (low reluctance), lots more of the magnetic field gets shunted through the middle iron. Resulting in even less magnetic field coupled to the secondary.