When you go to Apps and Books > Public > Add Application > Enter URL, this URL would be the URL of the application in the Google Play store. Not the URL for a web application. Web Apps can be added in the Managed Google Play store.
Quick overview on how I do it:
To start, browse to APPS & BOOKS -> Applications -> Native -> Public and click ADD APPLICATION.
Platform: Android. Source: Search App Store. Name: Leave this blank. Hit Next.
Click on the Globe icon on the left side of the screen for Web Applications. Click the plus sign and fill out the information and click create.
Click on the newly created web app and then click "Select." Click "save and assign" to assign it to your devices.