Reluctance here is the resistance to a magnetic field offered by an air gap. One pole piece of a magnet is split through a pair of coils to twin faces, in proximity to which is a ferrous moving member linked to the stylus and connected to the other pole. Movement varies the air gap between the member and one face, hence also the magnetic flux through the circuit and coil.
"It's a miracle. When I took a look at my very moldy old 45 rpm record that my college singing group recorded almost a half-century ago, I thought I'd never be able to hear our golden voices again (including the fact that I no longer have a record player). But I sent you the record figuring that the worst you would do is send it back to me with ..."