Why is an external service via internet, e.g. web-push with GCM needed for service workers to push notifications?

I am doing this tutorial, but it doesn't work on the VPN of my company:

https://pusher.com/tutorials/push-notifications-node-service-workers

I am writing an application with a restrictive internet policy here. Apparently no external service like GCM can be used. However, for push notification web-push is used. Web-push uses GCM to send notification.

It seems like my company network doesn't allow GCM to send messages. I wonder why an external service like GCM is needed anyway. Isn't the cool thing about service workers that you can use them offline? What am I missing?