Why was a light fixture installed with dry wall anchors?
I am with everyone's opinion that we can't explain why someone install something wrong. Other than he did not practice standard installation practices, and that probably means that whomever installed the fixture was not an experienced electrician. 

What I can tell you is that all of the necessary parts are there in your pictures. First your box looks ok. You can see a lug attaching to the box at the 1/2" knockout in the back indicating a brace. also you have the mounting plate for the fixture. That's the round thing with all of the slots and holes in it. You will find that one set of those holes and slots will line up with the screws in the ears of the box. Then another sets of holes will line up with your fixture.

What I don't see is the ground coming from the box. I hope whoever installed it didn't just cut it off, because that need to be connected up also.

If an electrician or an electrical contractor you need to contact them and have them make it right and if they don't file a complaint the your AHJ.

Good luck.