Who first shortened the word "application" when referring to software? Maybe someone in the '80s, or earlier?

Looks like it's attested by '92.

App is shorthand from application, no known person "coined it", because that term is going back to eighties or earlier. Apple had MacApp (which was application framework) in 1985, that time app was already well known shorthand, for example Atari had file extension .app.

Unrelated, but TOPS-10 operating system had executables named with extension .exe, that happened somewhere in 1967-1970. TOPS-10 had lots of interesting stuff, that later is similarly done by newer OSes. Probably my favorite is ctrl+t, which sends SIGINFO in FreeBSD, giving you status from current running program. And what we see in TOPS-10 manual: "When you type CTRL/T (control-T), the monitor prints status information pertaining to your job on your terminal."

:)