Unlike what other commenters are saying, this Zout == Zin is applicable to audio.
For a fixed Zout much higher than zero, if we want to suck the most power out of the amplifier, we should use a matching Zin indeed. E.g. if an amplifier has 16 ohms output impedance, then we will draw the most power out of it with a 16 ohm load.
Loads higher than 16 ohms will result in less current flowing.
Loads lower than 16 ohms will cause power waste in the source impedance. For instance a zero ohm load will mean that all the power is dissipated in the 16 ohm source impedance: the zero ohm load draws current, but no power because it I^2R is zero.
So from there, if we increase the impedance gradually, we obtain more and more power until we get to 16 ohms, and after that less and less power.
In amplifiers we care about efficiency, not with operating at the theoretical point where absolute maximum power is drawn. With a near zero ohm output, we ensure that all the voltage is dropped by the load rather than wasted in the source.
When we have a near zero ohm output impedance, Zin == Zout still applies! E.g. theoretically, the maximum power transfer from a 0.1 ohm amplifier would take place if we connect it to a 0.1 ohm load. And that reflects the trend in low-output-impedance audio amplifiers: the lower the speaker impedance you plug in, the power power you get: 16 ohms, 8 ohms, 4 ohms, ... You just can't go anywhere near 0.1, due to the practical limitations in the amplifier: ability to deliver current without frying itself.
But, so yes, Zin == Zout is relevant, but in the majority of the audio amplifiers built, which have very low output impedance, that theoretical point occurs at low value of Zout/Zin which usually out of reach of the absolute current delivery capability of the amplifier.