Are Mach Diamonds radially symmetrical? Videos like this show a form that suggests a radial symmetry in the gas jet.  The same is reinforced by schematic illustrations.
But other images, like this, look like there is a twisting structure to the flow. (e.g. the flow is following field lines, or gaining some other accumulated bias due to them)  
Specifically, I mean that it could be seen as a ribbon (a flat strip, twisting; i.e. a helix)


In the latter case (as detailed here), I wonder if the "plasma" qualifier has a significant relationship to a (possible) helical flow.  Or, maybe this is a picture of a helical flow, but it's not dependent on being a plasma.
I am by no means qualified in this area, just curious about what I see and well-read enough to read proper journals.  I have turned up some potentially relevant information, here, but haven't digested it, yet
 A: Theoretically, the radial distribution should be symmetric. However, in jets in general it is well know that there will be a transition from purely laminar (i.e. symmetry preserving) to purely turbulent (breaks the symmetry). Have a look at this video. 
The presence of the plasma induces the turbulence at much earlier in space compared to when it is absent. Have a look at this paper. The fact that turbulence is naturally a stochastic phenomena, that means the radial symmetry will be lost for sure. What the plasma does to induce turbulence is called the Electrohydrodynamic Forces or EHD force for short. Those forces are exerted by ions in the plasma on the neutral flow causing it to change its characteristics. Have a look at this paper for more information on EHD forces.
In the particular picture you show here, it looks like a helix. To confirm one needs more pictures. If it is definitely a helix I would say there is something behind that. So we need more information about the particular conditions of the discharge to explain in more details. But I hope I clarified why the radial symmetry is lost.
Hope that helped
A: There are several questions here so I'll start with the ones I am most familiar with. 

I wonder if the "plasma" qualifier implies a different nature of flow than occurs from a typical jet engine.

In a plasma a portion of the particles are ionized so they react to external magnetic and electric fields. At minimum you probably have the earth's magnetic field in the experiment's pictured (unless they were canceled out in some cleaver way). A particle under some force $\bf{F}$ will have a drift velocity both perpendicular to the force and magnetic field direction $$ \bf{v_d}=\frac{\bf{F}\times\bf{B}}{\sf{qB^2}}$$ where q is the charge of the particle. It is clear that this does not happen in a jet engine where the particles are neutral. Here is a video showing a plasma reacting to a magnetic field. So to answer this part of the question, if the plasma is flowing (being accelerated by some force F) parallel to the magnetic field then there is the possibility that it may be radially symmetric along the axis of the nozzle. 
In addition to this effect, the particles in a plasma interact via the long range electromagnetic force so that effectively all particles within a Debye length interact with each other. This will change certain transport properties such as the diffusion length, conductivity, friction, ect. 
I hope this gives you a good idea of how the flow of a plasma might be different from that of a fluid. 
