I wonder how they will keep the waveguide free of contaminants and >1/10 wavelength irregularities that dissipate power over such a long transmission line relative to wavelength. They're starting from only 10kW from a single gryotron but absolute power isn't the real issue. They can always just incoherently combine many since it's not for communications but even doubling the power twice isn't going to get you past the number of 3dB (half power) losses you'd get with an improvised borehole mm-waveguide 10km down.
The extremely long low loss underground mm-wave waveguide would seem to be their first problem to solve.
I assume they'd have a drilling pipe down which the mm waves would be directed. It would also carry down gas to blow the recondensed rock dust back up. The inner surfaces of the pipe segments would presumably be lined with a smooth, very conductive material.
The extremely long low loss underground mm-wave waveguide would seem to be their first problem to solve.
Edit: https://publications.mygeoenergynow.org/grc/1034509.pdf is okay and on page 5 of 16 in Fig 2 you can see how they propose using purge gas down the waveguide segments to keep it clean.