The plasma shock weapon seems to depend on creating a fast-moving "brick wall" in the path of the oncoming vehicle. This would destroy any aircraft that depends on wings etc, no doubt. But what I wonder about is, what will it do to a vehicle that is already built to go through exactly those magnitudes of pressure/temperature waves.
Yes, shocks coming from odd directions could seriously affect the trajectory. Most warhead gizmos that I have seen (only in pictures) are essentially hemisphere-nose followed by a conical afterbody, ending in a blunt base. I don't know which way they re-enter: if it was a space capsule for soft touchdown they would want to decelerate quickly, so the base faces the wind and generates a big shock. But a warhead should come down ASAP, so probably the nose faces forward, and must be built for extreme dynamic pressures and heating. I don't know about the rest of the body, but the weight penalty for building all of it for high shock stresses should be small compared to the payload mass, I would think.
If shocks are likely to come from odd directions during final descent, I would redesign the warhead/descent vehicle to be essentially spherical, with maybe some jets that can be operated for last-minute trajectory corrections. That would be end of that technique, except that the ball can be deflected a bit and hence it would wipe out, say, Nagpur instead of Mumbai. Not very comforting.
So I don't yet see why this would be an effective weapon. On the other hand, an explosion from using explosive on a missile, is also mostly a detonation wave, so one could ask why that would destroy the vehicle if it is immune to hypersonic blast waves. The answer has to be that the thermal effects are even worse in this case. Or maybe it is the sheer suddenness of the shock that sets up fatal vibrations in the warhead's structure and breaks it apart.
Direct impact of a solid piece from an explosion, of course, is another matter, but requires getting a missile into the exact path of the oncoming warhead at a high altitude, in time.
As for the beam generation etc., once the right frequency is found to cause the interesting effects on air, I would say that computation speed is the only real barrier. You can get speed-of-light return of information along the entire projected beam path, so the information is there, to reconform the transmitting antenna (an electronic phase-shifting process, not mechanical deflection) so that the desired end result is achieved despite atmospheric turbulence, vehicle maneuvering etc.
The major advantage of the beam weapon is that it can swing around through huge distances, and stop on a dime, without being constrained by the acceleration and force required. But heating the air should take some substantial time (so does an explosion, so it's not a relative disadvantage, necessarily).
You have to do the image/signal processing at truly incredible speeds, though. This is the real limitation. But that has already been solved in the airplane-based boost-phase intercept business.
For the air heating weapon to work, there is another condition: It must be a nonlinear effect. In other words, absorption of that frequency must be very very low, as long as the beam intensity is below some threshold. But at the focus, in a very small region, the intensity goes above this threshold and causes breakdown of the air into plasma (electrons get stripped off). Once this starts happening, it must happen at an incredibly high rate, and ALL the energy is absorbed into this region.
This is plausible. It is the concept behind lightning in some ways - why lightning bolts occur through extremely thin tubes where electrical conductivity becomes very high (some similarity also to tubelights, where most of the energy is efficiently delivered into the electronic excitation modes). The secondary benefit (or maybe primary benefit) may be that it causes such a high electrical disturbance that it finishes off any guidance circuitry inside the warhead. The critical beam intensity level for microwave / millimeter wave beams to break down air, has been reported in 1980s papers in the public domain as being around 1GW energy input (which requires a massive power source on the ground for each beam). Maybe they have found some wavelengths where much more interesting things happen.
Anyway, interesting stuff for ppl studying nonlinear effects on air. Call them "GigaTubelights"