What does the “listen distance parameter do”?

The “listening distance” is basically an Air loss control.  What it does is as follows.  It is a Variable-Q lowpass filter - LowPass12dB with a parametric eq boost.

From acoustic text books we know formulas for the roll-off of air loss, given distance, temperature and humidity.

The "airloss filter" boosts the HF to fight off the loss.

In the following graphic the red rolled off curve is the predicted airloss at 100 feet, the top curve is the "airloss filter" and the middle curve, orange, is the product.  

The further away the distance, the lower in frequency the peak of the filter, since further distances attenuate lower HF values.  The brown curve is the airloss filter at 200 feet vs. the green curve at 100 feet.