There are two reasons why speaker cables are not shielded/screened:
The signal is so powerful that any interference would not be noticed.
Speakers are not very sensitive; it takes a lot of power to create sound on a speaker
This is why speakers are connected to an amplifier.
Input to amplifiers are very sensitive and so input should use shielded/screened cables.
P.S. If you have a 100W amp the good ones use about 48V. So you have at least 2A, with peaks higher. Peaks might hit 20A but for a very short time. To hear this your speaker cable needs to be thick.
It's not going through you.
According to your drawing, the reason this works is actually the opposite of what you intuit. The audio signal isn't going through your body. It's going through the wire.
The output from the PC audio port is AC-coupled which means that it is pushing and pulling on the mobile charges in the wire with an electric field, not direct conduction. More simply, there is a gap between the wire touching the PC's internal amplifier output and the pin of the audio jack where your wire is connected.
In order for the amplifier to receive this pushing and pulling on the charges (the audio signal), everyone (PC and Speaker's amplifier's input) has to agree on what zero means (e.g. no pushing or pulling). In physical terms, this is the point where the speaker's diaphragm is in the center (neither pushing or pulling on the air) -- where it sits without power.
To provide this "zero" (we call that the reference potential or just "reference"), the second wire is included in the cable.
When you only connect the signal wire and not the reference, the amplifier receiving it doesn't actually perceive that the signal is being pushed or pulled on because the entire amplifier moves up and down. It's like being on a perfectly smooth and flat surface while standing on a skateboard and having someone pull you on a rope. All of you translates.
But if someone takes you off the skateboard and then pulls on the rope, your feet are stuck and you fall forward (you feel the rope pulling on you relative to your feet).
In your audio case, your body contains a giant mass of mobile charges. When you do not touch the reference contact of the audio connector (the area at the back of the TRS plug closest to the plastic overmoulding) it is in contact with air which has almost no mobile charges and it's like standing on the skateboard. When you touch it, you add (electrically) your entire body worth of mobile charges. This is a stable enough reference to allow the amplifier to see the wire moving as distinct from you moving.
This effect is the basis of Capacitive Touch Screens.
My explanation is an accessible approach to understanding how capacitance in general works. A similar situation to the one you described explains how capacitive touch screens work (as are found on modern smart-phones, like the iPhone).
The screen is transmitting the equivalent of an audio signal all the time and you touching the screen adds your body's mobile charges to the picture and distorts the screen's "audio" signal. It is this distortion introduced by your finger that is detected, not your "touching" of the screen. That's why capacitive touch panels don't work well (or at all) with gloves or when your fingers are wet. These conditions change the way your finger distorts the electric field and confuses the detector.
Best Answer
First, let me give you a little background on myself, so you can "know the source"... I'm a Sr. Electrical Engineer working in the Professional Audio field. I design high end pro-audio equipment. You've heard my stuff, as it's been used all over. I have also designed stuff for a small "audiophile" company. I'd also call myself a Skeptic, and a practical person. My pet peeve is worthless pieces of expensive audiophile junk. That being said:
There are two ways to approach this: Does it work? and Is it worth it?
Does it work: Yes! Um, no. Well, maybe. It depends on what you define as "work". If you define "work" as "can it, in theory, make a positive difference when compared to normal speaker cable" then it does work. But if you define work as "makes a positive difference that an expensive piece of gear can measure, or that can be determined by multiple listeners in a double-blind test" then the answer is no.
Is it worth it: These things cost US $8500 and make such a small improvement that no one can really hear it (or can prove that they hear it). A good pair of practical speaker cables will cost about $30. For the $8470 price difference, what could you buy that would make more of a difference in your life/happiness? A vacation to a remote tropical island? A semester in a University? The ultimate man-cave? With these speaker cables all you get is bragging rights that you can blow lots of money. Get spinners for your car, they'll attract more attention that speaker cables. So, um, no. They aren't worth it.
Here's an interesting article about comparing expensive Monster speaker cables to a wire coat hanger. Spoiler: The coat hangers work quite well.
The ideal speaker cable is short-ish, reasonably large (but not absurdly large) gauge, and set up as a twisted pair. Nothing else really matters.