On one of them, I downloaded the latest version of the VASSAL ENGINE, intending to upgrade it from 3.2.12 - the other is already at 3.2.17 from a few months ago.
Anyway, when I launched the .dmg file I got an error…
VASSAL-3.2.17-macosx no mountable file systems (see image).
I checked on my other system and got the same error (even though that machine was already at 3.2.17)
I downloaded archived versions and ran those on both machines - same error.
I attempted to run other .dmg files from other providers - these all worked, without error.
My conclusion is that either the vassal engines .dmg files are corrupt or not compatible with this version of macos.