IOS: Not Running State

The terminology in the article is a bit confusing but if "backgrounded" is intended to mean "apps that are hidden by the Hide command", there is a way to represent that with a hidden preference:

  defaults write com.apple.dock showhidden -bool true
  killall Dock

When an application has been hidden its Dock icon is then given a semi-transparent, faded appearance.

Also, although Mac OS X Lion changed the Dock so that by default there is no difference between running and not running, using System Preferences (Dock pane) the "Show indicator lights for open applications" setting can be turned back on.