I would like just to add something:
Purely speaking, StaMPS itself are the matlab scripts (found inside the matlab folder within the stamps package) for doing PSI/SBAS/MTI , which obviously runs on MATLAB and hence, it should work on Windows, Linux or any other platform in which MATLAB runs. (please note that snaphu and triangle should be also installed in the system and included in the path).
The rest of the scripts provided within stamps package, are for the interferogram computation and SAR SLC image coregistration and resampling, that must be done previously to StaMPS. Currently there are different options to do this part that works also in Windows, such as for example you can use SNAP (v6.0) for doing the interferograms compatible with StaMPS PSI (and you can use the snap2stamps script for doing those interferograms automaticaly) . See the thread : Snap2stamps package: a free tool to automate the SNAP-StaMPS Workflow
The mt_prep scripts, that are used after interferograms and before StaMPS, which translates the interferograms in StaMPS compatible input runs on linux or similar (as they are bash/ctsh scripts using other functions) , and then you could face some issues as indicated by @ABraun before.
But if your plan is to do everything (interferograms + PSI/SBAS/MTI) using only the stamps package, then the answer is the same as given by @ABraun.
Cheers