Is there a layman's explanation about what the advantages / why there are advantages here?
It talks about turning off the plasma antenna, is that any different than simply not using a regular antenna? ... or what they mean by stealth or "resistance to electronic warfare and cyber attack".
When the plasma antenna is turned off, it stops existing. There's nothing there to attack or detect.
A possible future advantage would be shaping the plasma with magnetic fields, to create customizable antenna geometries, or geometries that electrically extend beyond the physical bounds of the equipment. Imagine using a laser small enough to fit in a backpack to create a 1/4 wave antenna long enough to transmit or receive at 30 kHz, with length 2.5 km .
You could create a plasma antenna 2500m long, send a message to a submarine 150 m below the surface, then it just disappears when you turn it off.
It would be unlikely to glow brightly enough in the visual spectrum to see in the daytime, but it would be pretty cool at night.
This, however lets you dynamically choose the antenna length, and each frequency has a perfect length that works best for it.
So the two are complimentary, but at different parts of the process.
Did you even read the article? They mention Solid State Plasma antennas, which can be fabricated using standard silicon chip fabrication techniques.
For security applications, the ability to turn it off is kind of nice; no antenna = no backscatter. OTOH how stealthy can a plasma antenna be when it is on?