Single-Sideband Suppressed Carrier Demodulator
No, it is not a ring modulator: it is a Single-sideband Suppressed Carrier Modulator/Demodulator (or Frequency shifter).
With this module, not only the carrier, but one of the sidebands is suppressed, so that the frequency components in the output of this device consist of either the sum or the difference of the carrier frequency and the frequency of the components in the modulating signal.
Note: all output signal components , except the desired demodulated audio signals, are filtered out: no standard offset adjustment is required. If the LM1596 is not available you can use the LM1496, but check the pin assignments.