To understand how bits correlate to sound quality, an understanding of dynamic range is needed. Dynamic range is the ratio of the biggest signal that can be generated to the smallest. With a digital signal, the smallest producable signal is 1 LSB and the largest is full-scale. The dynamic range of a digital signal (in dB) is 20*log10(2^(#bits)); this is roughly 96dB for a 16-bit signal. This means that if an ADC has 96dB of dynamic range, but the data path is 20 bits, the four LSBs (beyond 16 bits) will be in the noise and won’t contribute meaningfully to the signal.
From the data sheet of the 9880A, the DAC has a DR of 96dB and the ADC has a DR of 82dB. Thus, no data is lost using the 16-bit DAC.