As you mentioned it is purely theoretical so far. They transferred the math from existing and proven phenomena of "waves behaviors" from other fields to the electrostatic interactions between particles inside a plasma.
The main idea of this paper (for what relates our interest) is to establish a mathematical framework to "theoretically prove" that the plasma oscillations due to the electrostatic attraction and repulsion of the particles inside the plasma itself can be forced to behave as self confining structures that are independent from the plasma conditions within defined ranges.
In practical terms that would mean that there will be no uncontrolled electrostatic oscillations inside the plasma, and thus no instability that would disrupt the plasma confinement.
It goes without saying that such a feat would be a giant leap for plasma control and fusion applications in general, but even if they can prove it mathematically it does not mean that it will ever be possible to obtain such a result in real world.
At least for now (at the best of my knowledge) we are nowhere near the technological level needed to control electrostatic waves inside a plasma.
Maybe someone will take over the challenge in the future, so is worth to keep an eye on this field of research.
From wikipedia:
Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon.
From physorg:
One of the properties that characterizes a plasma is its ability to support collective motion, where electrons and ions oscillate—or wave—in unison. These oscillations are like a rhythmic dance. Just as dancers respond to each other's movements, the charged particles in a plasma interact and oscillate together, creating a coordinated motion.
From Wikipedia again
In physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the free electron gas density. For example, at optical frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton.
With my own thoughts and in my own words:
A plasmon is a macroscopic physical entity consisting of plasma. It is confined in space and time and has enigmatic double energy-matter properties similar to those of the photon.
The ones they demonstrate with diffraction gratings in basic college physics.
This work shows that, in theory, a plasmon is conceivable that can confine particles of any energy without being affected? The problem is how to create that plasmon?
Correctly understood?
Perhabs they have stumbled on the solution to the ball lightning problem?