Windows is the first thing I can think of that used the word "application" in that way, I think even back before Windows could be considered an OS (and had a dependency on MS-DOS). Back then, the Windows API referred to the Application Programming Interface.

Here's a Windows 3.1 programming guide from 1992 that freely refers to programs as applications:

Common dialog boxes make it easier for you to develop applications for the Microsoft Windows operating system. A common dialog box is a dialog box that an application displays by calling a single function rather than by creating a dialog box procedure and a resource file containing a dialog box template.