I used to simply assume that the Quiz was weird because you couldn't set the grade.
I've been using Moodle for 15 years and I didn't know about that setting. Just sayin'. I would look for the grade setting in the Grade section of the activity settings. Where it is for everything else.
Making not have a grade if you set it to zero is an interesting thing too. That's the sort of thing that makes sense if you are a developer but, possibly, nobody else.