Still sounds rather dubious. I dunno about this whole thing about the beam creating a protective glass wall, but I'll give them a pass on that. Also on how they'd actually evacuate all the fluid and how they'd extract ash and fumes without it. The most critical part sounds like heat. It's very hot down there, and we're also presumably running megawatts of electrical power for this beam, which all goes to more heat. Ambient temps at those depths may be over 300 F / 150C, and that's before we pump in megawatts of extra heat with no way to extract it.
I helped design and operate lots of oilfield electronics for those depths and temperatures. MTBF for the most hardened electronics we could get our hands on at temps over 150C was in the neighborhood of 200 hours max. Drilling slowly with much more sophisticated and unproven electronics, I expect they'll be dropping like flies if they ever work at all. And that's with extremely generous assumptions on the heat loads. MTBF of electronics drops exponentially as temperature goes up.