"How can I test that the right stuff is drawn on the screen? Either I set up a camera and write code that can interpret what the camera sees, or I look at the screen while running manual tests."

Or screenshots, of course, which is still relying on code obviously but probably not your code. Of course, defining what you're looking for in a screen shot is going to be nontrivial unless you're doing simple check that it hasn't changed from the last manually-approved version or something.