There are 3 ways to view image of  cameras on DVR system.

1. View on monitor doesn't need Internet. So a router is not necessary for view on monitor.

2. View on computer and phone need Internet. So a router is necessary for view on computer and phone.

But please notice system is not connected to computer or phone directly by cable. System is plugged into router to connect Internet by ethernet. Phone and computer is also connected to Internet. Finally, phone and computer can use Internet to connect system.