Looking at this from the point of view of the TCP/IP network model, the connection establishment occurs at the Internet/transport layers. This needs to be device to server since most devices will sit behind NAT and firewalls. At the application level however, once the connection is established, the notifications are sent from server to device without the device polling so I would agree with this being called push.

https://theapplewiki.com/wiki/Apple_Push_Notification_Service