"Application" has been a common general term for an end-user program for a very long time, and "app" is just an obvious abbreviation that people and UIs have used to varying degrees all along. iOS apps merely mainstreamed the term, they didn't take ownership of it.
iOS mainstreamed it, but for a long time, "app" had a different meaning. Like, "application" was the big full-featured thing you run on your PC; "app" was the toy thing you run on the phone.
Then some "genius" started calling their desktop offerings "apps" (perhaps because lazy multiplatform-via- webap development eventually extended to marketing copy"), and now everything is an "app".
