So judging by
the Cirrus CS3310 datasheet, it looks like its use adds to the THD at the input and potentially increases cross talk. Also, because the CS3310 doesn't exclusively attenuate the signal, it could color the sound somewhat.
Honestly, the fact that it's bigger than a stepped attenuator would be my biggest complaint.
From what I gather, it works by having that microcontroller trigger some relays for source selection. The outputs of those relays are wired up to the appropriate pins on the CS3310. Internally, the CS3310 chooses (via a multiplexer) the appropriate resistor values for the feedback loop and source of an internal opamp to give the correct attenuation or gain. The output from the CS3310 is then exposed as through-hole pins on the board.
This works based on the same principles used to set the gain in opamp based amplifiers, such as the CMoy. To use the CMoy as an analogy, in reference to
Tangent's CMoy schematic, R2 and R3 are selected by the control register of the CS3310 and potentially some other internal logic.