More like straight out even though the manual said to lift up.
I have tried pushing the prong from a 90 to a 45 angle but it does not budge. Both sides of the door came off this way. I believe the only way I can put the door back on is to change the angle of the prong that goes into the stove so the notch can catch. The video refers to a difficult type of hinge. There has to be a way to move the prong into the right position.
The picture is you hinge though. You are right that the prong need to be pushed down of else the door will never go back on. There isn't a video of your exact hinge but yours is close to that. Here is a better video of your problem. CLICK HERE