I don’t use Roger so I have no experience with the Roger Updater. However, most firmware update programs run on Windows and won’t work on a Mac unless the Mac is running some virtualization program such as Parallels or running Windows under Boot Camp. I run Windows 10 on an iMac Pro using Boot Camp in order to run the programming software for my Oticon aids. The firmware updater part can update firmware in the aids or in accessories like a TV Adapter or ConnectClip - this requires Windows.
A Mac should be able to download most any file unless the web site checks to find out the OS of the machine attempting to download and then offers downloads for the appropriate OS only. A Mac can download a zip file - in many cases the zip file is unzipped automatically and the results ends up in the user’s Downloads directory. If the file name of the unzipped file ends with .exe, it would probably run only under Windows.