Fascinating... wikipedia mentions using nuclear power to achieve the 1300-1700C temperature needed for the rock melting. (BTW, the smooth glassy tunnel is a byproduct of that). I wonder if you could achieve the same thing using plasma arcs (http://en.wikipedia.org/wiki/Plasma_Converter), then somehow use the pressure and heat of the earth, once you're deep enough?
I wonder how Shaped Charges would perform. They're relatively inexpensive, would easily produce the temperature needed for glassing the rock and have excellent range penetration. A single shaped charge can easily penetrate beyond 10 times its diameter.
Based on the Beach Pneumatic Transit diameter of around 2.5 meters, a single shaped charge designed to penetrate at this width (cone diameter of around 2.5 meters) would easily penetrate between 25 or 35 meters. Although on such an industrial scale, I wouldn't doubt some military contractor would go commercial with one that could penetrate up to 50 meters.
The question would be, could such a destructive method (on the small scale) be more useful than current explosives used. There would likely be less shockwaves sent through the rock than traditional mining techniques, plus the potential glassing could help structural strength.
The use of something so easily mass produced like a shaped charge could easily be used in vac-train mining like this. Although personally, I doubt any system like this would ever be used between continental plates.
