I am curious as to why it needs any circuitry on the ground line - would a direct connection not work? (I guess I am assuming that L, R and ground are the only connections made to the headphones.) Do the amplifiers put a DC bias on the L and R outputs that needs to be matched on the ground, and if so, would a capacitor in series with the L and R outputs not be enough to isolate it?
You could just use the middle connection between the two batteries as a ground. I'm not sure why he didn't do it. Perhaps so that the whole thing works longer even if one of the batteries is discharged faster. That would be my guess.
As it stands, 40% of its 23mA current draw is through the 1kΩ x 2 voltage divider... Now I am wondering if a circuit with the between-battery link connected to ground would risk damaging the op amps (or phones) if only one battery was in?
