Yes, you can call it a spatially-resolved FTSI, that's correct.
There is a whole field of research around FTSI hyperspectral imagers.
The big challenge is to get fast enough to get a decent time-resolution.
To explain why this is „suddenly“ about time-resolution: the mirror on the translation stage is moved back and forth which changes the length of one arm of this interferometer. This movement takes time but is necessary as the interference pattern changes with position of the mirror. These changes are recorded and allow to compute the spectrum. Since the scanning takes time, this limits how fast images/spectra can be recorded.