To understand in which direction the forces on the door we must appreciate the following.
Forces on a door hinge physics.
Back to door design what really jumped out at me was how the forces on the door hinge were concentrated over such a small distance and are much closer to the floor than most doors.
By its construction in can apply forces perpendicular and parallel to the surface.
The pin can propagate force in any direction.
The hinge is a hinge.
Your graphic shows the pin in the hinge.
The hinges a and b are symmetrical placed at the corners of the door and each supports half the weight of the door.
The force of gravity acts on the center of mass of the gate but the hinges act on the left edge.
We conclude that the turning effect or torque of a force depends on the magnitude of the force and the perpendicular distance between the line of action of the force and the pivot the hinge of the door in the case above.
The forces f in each hinge are equal.