Shielded vs Twisted cables
If you have a balanced audio signal (e.g. XLR), then the idea behind a twisted pair is any interference that one wire picks up will also be captured by the other wire.  The device that receives the signal only cares about the difference between the two levels, so any common mode noise can be ignored.  This is extremely important for long runs (lots of opportunity for noise to intrude), or microphones (very low signals).  Good cables will also be shielded, as the wires aren't "perfectly twisted" with zero area between them, so are still slightly susceptible to interference.

However, with unbalanced audio (e.g. phono plugs, jack plugs, TRS (like your picture), etc...), you only have one conductor, so must totally shield it to prevent noise.  Still, such runs are both short and amplified, so the effect of interference will be smaller and is generally inaudible.

A "braided cable" like the one you picture is probably electrically worse than a typical foil-shielded audio cable.  Such a braid would also be counterproductive in balanced audio as the conductors are unnecessarily separated.

As for why they are braided that way, it's because it looks kewl (so they can charge more), and in that 6" cable, nobody will ever hear the difference.