Is this a Miller integrator?
Yes, that is a Miller integrator.  But ...

Compared to an opamp. a 1-transistor common emitter amplifier has less gain, a higher input (equivalent) input bias current, and a higher output impedance.  These combine for a circuit that is a less accurate integrator.  That is, the integration time constant is not simply R4 x C1.  To start with, the R for the time constant is the Thevenin equivalent of R1, R2, R3, and R4.