See here for a good explanation of quasi optical transmission: https://www.bridge12.com/learn/what-are-quasi-optics/
How is it going to displace molten rock after it is softened?
And, if it's too hot for drill bits, how is it any better for electronics, power conducting cables, and cooling apparatus?
It seems like hammer technology in search of nails like flying cars and battleship rail guns.
One thing I do know is conventional microwaves heat the bejesus out of the edges of silicon dioxide objects like glass containers and ceramic bowls far sooner and better than they do food. Perhaps they have a dipole moment similar enough to water that it's unavoidable and typically enclose tasty vittles from spilling and sloshing all over.
Getting cuttings out of the borehole is a solved problem with present drilling technics used in the Oil & Gas industry or geothermal. The drilling fluidsbrings them back. One needs the drilling fluids (mud) to avoid the well to collapse, I guess Petra is staying clear of deep borehole drilling because they can't operate their technology with drilling mud present. Also the deeper you go, the smaller the hole and they may face miniaturizion issues too.
The only way I could imagine this working is to lower the gyrotron itself down the borehole, but there's presumably tradeoffs of physical dimensions and output power that make it challenging. Again maybe not impossible, but there's no indication they've made fundamental advances in miniaturizing the source, or producing lossless waveguide.
Related, another interesting company I came across is Petra [2], who is doing something similar -- plasma/heat based non-contact drilling. But because they fracture the rock instead of vaporizing it, there's essentially gravel/sand leftover which is hard to evacuate from a deep vertical shaft, hence their focus on power/fiber trenches not geothermal.
[1] https://www.nrao.edu/meetings/isstt/papers/2012/2012151153.p...
[2] https://petra.cc/