While some power can be sourced from parallel ports for some applications, in general, I think there's a lot of incompatibilities when doing so.
For instance, when powering some SPI EEPROM or small microcontroller for parallel port "dongle" for software activation, at least there you have a specific software handling the parallel port in specific way. For instance idling data pins high a lot for power harvesting into storage cap, and only shortly transfer data so the cap voltage does not drop too much. And even then those did not work on all computers..
But for general purpose covox application, there is no standard in what way they set the control pins, and since the data is audio, there is no guarantee how much on average the bits are low or high to provide power. Also parallel ports from different eras have different output stages so the logic levels might be 5V or 3.3V to begin with, and early logic chips had pretty high output impedance, so the voltage will fluctuate a lot depending on how many bits are turned on (when harvesting power from them that is). So for R2R DAC + opamp, I don't see a general solution that would work well on all machines, even if it does work on certain parallel ports with strong output drivers. And because of the high output impedance of the data pins, wouldn't that also change audio amplitude depending on how many bits are on, so that would distort the audio as well (unless it's a DAC chip).
Having said that, the Covox patent did include designs that harvested power from parallel port and had a transistor as emitter follower (buffer amplifier). But did they produce any buffered designs, I have no clue. If not, chances are they found out they don't really work, which is why the plug came with externally powered speakers so they can have the amplifier there. I believe some early designs had two wires from the speaker to the plug, the other carrying power for some electronics in the plug.
Fortunately, much more power for active covox plug can be harvested from elsewhere, like keyboard/mouse/joystick ports, serial port..