Hiya William.
Wow, SuperMorse! The first time I came across that program was when it was given away on the the February 1995 edition of Ham Radio Today magazine (I think I still have the floppy disc floating around somewhere here).
You're quite right about it being a DOS program (DOS = Disk Operating System). Although MS-DOS (Microsoft DOS) is possibly about the most famous system, there was also IBM-DOS, and maybe a few other ones too.
I had a look around the web because I'd never heard of anyone running DOS programs on Android, but amazingly it is a 'thing'. The program (or 'App') you require is called "Magic DOSBOX", and you can find it here:
https://play.google.com/store/apps/details?id=bruenor.magicbox.free&hl=en_GB&gl=US
There is also another DOS emulator for Android called "DOS Box Turbo" which you can find info about here:
https://sites.google.com/site/dosboxturbo/home/beginning-dosbox-turbo-for-newbies
If you search Google etc, for "dos games on android", or "android dosbox" and so on, you will find a good number of links to sites showing how to install and use the various DOS emulators on your Android device.
Once you have an emulator running you can then install your SuperMorse program via the DOS emulator program (emulator programs simply convert the DOS code into something that Android can understand, and vice versa, think of it as a 'translator' between the two systems).
You may find that there is a modern equivalent of SuperMorse already written for Android, the web seems full of Morse Code Apps these days!
73, Mark...