I think it's helpful to derive the literal meaning of PCM.
The process of multiplying two signals is Amplitude Modulation—AM. If one signal is a constant 1, the other passes though. If 0, no signal passes, just a constant 0 value. In between values modulate the amplitude of the other input—amplitude modulation.
Analog sampling—taking a measurement at a regular interval—is equivalent to AM of the signal with a pulse train. Another term for this is Pulse Amplitude Modulation—PAM:
Since the pulse train is 1 for an instant, we get the signal value at that instant, but 0 at all other times.
For digital audio, we save only those instantaneous values, the only information we need to reconstruct that PAM signal, since it's zero at all other times. We encode the instantaneous values into a numerical values. That's the C, "Code", that replaces the Amplitude in PAM, resulting in Pulse Code Modulation—PCM.
So, whether you stream it or hold it in memory, those sample values represent the pulse-code-modulated signal. As long as you have a series of digital values that represent the amplitudes of the pulses emitted from the PAM process, it's a PCM signal.