The point is that the screws don't screw into the door, they screw into the other half of the knob assembly. You can see one of the sockets in the picture you show -- it's the tube sticking out in the hole.

Normally, a complete circle is hole-sawn out of the door. What you have there is amazingly slapdash.

https://www.thisoldhouse.com/home-safety/21016489/how-to-install-a-lockset