It is not called a two-stage amplifier in any common usage.
It is a single stage differential amplifier because there is a single node where voltage gain occurs -- at the drain of MN1. The signal there is the difference of the signals at the gate of MN1 (directly), and MN2 (via the PMOS current mirror)
When you calculate the gain and the input impedance of the shown circuit - in particular for unsymmetric operation with Vin1=0 (or Vin2=0) - you can treat the whole device as a common-drain-common gate combination.
Hence, it is not wrong to say that the system acts as a two-stage amplifier.