"Note: the app will be running in an environment where there is no Internet. Hence push notification will not work here."

Emphasis original.

The author did not say they have no network connection, they said they have no Internet connection. The two are not synonyms. This makes perfect sense. It is factually wrong to laugh at that.

Now, it is possible that shiplu.mokadd.im is using the terms synonymously, but the text of the question leads me to believe that it is entirely possible that a local network resource is being used over Wifi and that he understands this quite well.