I ran the point density tool and got an output, but because the 'Area Units' option in the Point Density was locked to Square_Map_Units - I don't know how to tell what units the density was calculated with, and no way to convert that into density/km2 which is my desired output.
Based on the tool (Point Density) that:
If the output units is anything other than feet or meters, the output area density units will be set to SQUARE_MAP_UNITS. That is, the output density units will be the square of the linear units of the output spatial reference.
if the output linear units is centimeters, the output area density units will be SQUARE_MAP_UNITS, which would result in square centimeters. If the output linear units is kilometers, the output area density units will be SQUARE_MAP_UNITS, which would result in square kilometers.