Voltage output

Why is dac and preamp output measured in voltage and not current?
Because the devices they drive are voltage sensing, not current sensing.

The two pieces noted feed devices with high-impedance inputs (say 50,000 or 100,000 ohms) that require virtually no current. The voltage reading dictates the operating parameters.

Contrast that to a low impedance device such as a 4 or 8 ohm speaker where the resistance is so low that current draw is significant.
...another reason is that music signals are produced by a transducer (microphone) which can easily and accurately follow and convert the sound energy into voltage. If you tried to do this with current, the internal resistance of the microphone and the audio playback equipment would have to be calculated to an extremely precise value - an almost impossible (and expensive) undertaking - to be useful. So it is easier to do voltage gain instead of current.