Let's back up a little. Let's look at how when you use a tensile element at an angle to the applied force the manner in which the forces in the tensile element can be multiplied. Because that's the core of this misunderstanding.

THis is a long one but I hope it's worth it.

I've done up another couple of diagrams (OH NO! NOT ANOTHER ONE! ) that hopefully shows where my spoke diagram thinking came from. In this a simple weight is suspended on a shop wall mounted cantilever beam for moving the weight around. In this case a free pivoting beam (C) is supported by an angled rope (A) and there's a second shorter rope (B). As you can see the (B) rope has a simple 100 lbs of tension in it. If we compare this to my spoke diagram rope (B) is the equivalent of the tangential spoke In other words the spoke is in line with the force being applied so the spoke only sees the simple load.

But when you force the rope off at an angle like with rope (A) and keep it there with a beam (C) it gets more complex. Now you end up with the load in the ropes trying to compress the beam. But we're also supporting the load with the rope (A) which is at an angle. What happens is that it's like using a lever to move a heavy object with a long arm and a pivot in close to the load. The weight is your effort on the long side of the lever and the angled rope is on the short side. The force is multiplied in the angled rope because the beam is translating the direction of the load.

Now we can certainly do this wiht trigonometry and drag out the sin's and cosines' but for this example the force of the weight is vertical, the compressive forces of the beam horizontal and that forms two sides of a nice convienient right angle triangle. And since the tensile force in rope (A) is obvioiusly in line with the rope we can use that angle for the third side. So we draw a triangle with the vertical side at a scale of 100 units and a horizontal line from one end of that line and an angled line of the same angle as rope (A) from the other end to form a triangle. That's shown above the diagram. From there we scale the lengths of the other two sides compared to the known 100 units side and we get the numbers shown. But note that both of these are significantly higher than the original 100 lbs. There's no additional forces being introduced. However note that a lot of the rope's tension is balanced by compresive forces in the beam. But the rope is still under 333 lbs of tension to support that 100 lb weight. The tension in rope (A) and compression in beam (C) are strictly due to the geometry of the suspending arrangement and the weight it is lifting. In effect I've just sketched out your hanging rope example where you push the load on the end of the line to one side.

This diagram ties in directly to the spoke loading diagram. The only difference being that there's no physical beam to hold the offset spoke at the angle shown. However that "wall and beam" are still there but it's the other spokes and the rim that hold the one shown in my diagram in place at the angle shown. In the triangle of forces I showed this support from all the other spokes and the rim would all resolve to the 28.6kg virtual line that is extended off the 9.2 kg vector at the right angle.

However in looking at the diagram I will admit that I put the arrow for that vertical "beam" compoment on the wrong end if you see it as a counter to the spoke force and being conatained by the rest of the wheel. On the other hand it's fine as it is if you look at the arrows in the triangle as broken down components of the tensile increase in the spoke.

So for the spoke angle shown can you now see how when you torque the hub with 9.2 kg per spoke and the spoke is at an angle to that force just why the mechancial "leverage" due to the angle of the spoke to the force is going to induce a tension increase in that spoke by so much?

Let's say the hook on the wall was too high up and for some reason the boss chose to make us lower it so the distance from the beam pivot to the rope eye ring is only 1/3 as much. This compares to our spoke getting closer to a true radial angle where the spoke is at or very close to 90 degrees to the tangential torque force of the hub. Note how the tensile load in the rope (A) just more than tripled to over 1000 lbs needed to support only 100 lbs of weight.

Why? Look at the arm length of the beam and the distance between the pivot and the rope(A) mount. Mechanical leverage. It's the same with our spoke that's trying to resist the forces that are not in line with the spoke. The spoke is acting just like rope (A) in the diagram. Actually as you mentioned first off we have 16 spokes all working together to resist the load but we broke it down so only one is being looked at. The "braking" spokes and the rim form the supportive wall and beam that hold the 16 pulling spokes at the angle we lace the wheel up for. In the case of my original spoke diagram the angle shown is probably not far off what a 1 cross pattern would be.