Writing SPI Flash on Mac
It seems that somebody has already written some software in python to interface this exact dongle (labelled WTX100, apparently a relatively popular, cheap SPI programmer), without needing any part of the original, closed-source software:

https://github.com/mytbk/xtw100

So you need python with the pyusb library, and then you'll probably need to tweak this program to your needs, but it seems you have the possibility to use your dongle from non-Windows operating systems.