Seems the notification is not working, or do I need to buy the
Growl from App Store in order to use it?
First, make sure you've read "Growl Notification from iTerm 2" on using Growl. If that doesn't work, here's a short history of Growl:
The older versions of Growl came as a framework and preference pane and were free. Applications with Growl support could not use it unless you installed Growl. Recently (version 2), Growl became a paid application through the app store. When this occurred however, it was no longer necessary to install it to use it. Applications linking against the new versions can display notifications without the application installed, but you won't have any customization abilities.
Therefore, if you cannot get notifications, either iTerm2 is using a version of Growl before it was paid, or defaults to having no notifications enabled. It is much more likely that it is using an old version, which means you can install the old versions available on the Growl website (direct link for the most recent free version). If you install that and still can't get notifications, then yes, you will have to purchase the application.