How could that be possible? Well, the website is nothing but a Flash file that needs an initial Internet connection to get download on the computer (the browser's temporary folder, to be precise). Once the Flash file is downloaded, technically, the whole website is now on your computer's hard drive itself.
Now, the next challenge is to be able to investigate whether you are connected to the Internet or not. This is achieved by constantly pinging a certain IP address on the Internet. In case the website manages to get a reply, that confirms the presence of the Internet connection and swiftly blocks the access to the website until the connection is severed again.
So, how does it work, again? When you visit the website at first, the website itself gets downloaded onto the hard drive. However, access to the website is blocked as long as the computer is connected to the Internet. And that connection can be confirmed by constantly pinging an IP address on the Internet. No reply means no connection.
I hope that solves the mystery behind the mojo of AllAboutRajni.com.