Is there a "first" Fourier transform?
Independently of what they call it, the process described in the paper is precisely the Fast Fourier Transform. This is made obvious by the FFT algorithm they describe, including the Gold-Rader bit-reversal procedure.

On a side note, if one tries Googling "SFFT", the S in the acronym stands for anything from sliding to spherical, but the F's always stand for Fast Fourier.