I also had issues running this under DOSBox version 0.74.3.0 with my OS being Win 10. The error I got was:
Load error: no DPMI - Get csdpmi*b.zip
I googled it and it seemed downloading cwsdpmi.exe was supposed to help but I got a page fault error after dropping cwsdpmi.exe into the same directory as MINESWEE.EXE. I downloaded from "https://dosgames.com/files/cwsdpmi.zip"