Is Microsoft Word is considered to be Application Software?

Linux

No, the Operating system, is the environment which is software based.

But this environment allows applications to run within it.

An example would be Ubuntu (which is Linux) Operating system runs a media player application program such as Banshee.

Microsoft Windows 7 Operating system running a Word editing application such LibreWriter or Microsoft Word.

Mac OSX operating system running iMovie an video editing application.

Applications are programs running in an operating system.