More generally, it is the ratio of the y-axis units to the x-axis units.
Peak area (y-axis) is most generally voltage X time, and so could be
millivolt-sec or
microvolt-sec (or any other combination of voltage and time units).
If the data system has done an intermediate calculation to absorbance, then the units would be
AU-sec or
mAU-sec.
Concentration (x-axis) could be expressed as mass/volume and so could be
mg/mL, or
g/L, (or any other combination of mass and volume units).
It could also be expressed in molar terms, in which case the units would be moles/volume.
Just to complicate life, the x-axis could also be expressed as mass-on-column, in which case the units would simply be mass.
So, the response factor (slope) could be mAU-sec-mL/μg (which is equivalent to what you wrote), or it could be:
μV-sec/μg ,or
mAU-sec-mL/mol , or . . .
It all depends on how your data system and inputs are set up.