Wow, I’m very pleasantl surprised that my hunch turns out to be completely correct 
They seem to be using a generalized form, and use the exponent as a variable parameter … iinteresting…
They’re not modelling the response of photographic paper, though, but that of the human eye, and derive a mapping to make HDR images appear as natural as possible. On skimming the paper, it seems that this includes local contrast/detail adjustments.
I may have to read it properly to make sure I’m understanding at least the gist of it correctly.