When you choose File -> Save (or Save As) the Automator action is automagically set up to run whenever a file system event occurs with that folder (hence the requirement to choose the Folder when setting up the action) courtesy of
The workflows themselves are saved in
~/Library/Workflows/Folder Actions/, which you can be opened up in Automator on other computers and applied to folders.
So there is no explicit way in Automator itself to save the action as an application itself but it is automatically run when the conditions (a file is added to that folder) are met.
Of note you can manage Folder Actions by either clicking on a folder in the Finder and choosing "Folder Actions Setup..." from the Action (Gear) menu or opening
Folder Actions Setup.app from