First, how do they plan to address well control? As you drill down through the Earth, you drill through many layers of rock, some of which contain oil and gas in various quantities. Since the thousands of feet of rock above is heavy, they are under a lot of pressure, and will be happy to flow out through your borehole and up to the surface if you don't take measures to keep the formation under control. If they are allowed to do that, those flammable materials can easily ignite and cause a fire big enough to destroy your entire drilling apparatus and be very difficult to put out. Note that you don't necessarily need enough oil and gas to be commercially produceable to generate a disastrously bad blowout.
Oil wells address this by filling the borehole with drilling fluid at a specific density, which produces enough pressure at the bottom of the hole to counter formation pressure. Every well is also fitted with multiple blowout preventers to seal off the well in case of a sudden pressure increase from the formation, and also allow heaver weight fluid to be circulated in to get back under control. The wells are also drilled and cased in sections, so that there is never too large of an amount of borehole uncovered that needs to be kept under control.
So given all that, exactly where is this Gyrotron going to be? If it's at the surface, how are they planning to microwave through miles of drilling fluid and have enough energy at the bottom to cut more rock? If it's at depth, how is this Gyrotron going to survive the high temperatures there? High-end electronics are much more sensitive to extreme heat than drill bits are. Especially if you're pumping ~megawatts of energy through them to actually cut rock. Speaking of, how would we even get that much electric power down there? Oil and gas has spent many billions of dollars on this and has yet to find a good solution.
Also, how are they planning to keep this whole straight and judge depth? Holes thousands of feet down don't just stay straight, you have to actively keep them straight. The oilfield has plenty of ways to do this with conventional drilling hardware, how will their Gyrotron system manage it? And we also need to transport rock cuttings / fumes to the surface fast enough to support the drilling rate, how will they do that?
I'm also wondering about fluid flowrates. If they manage to drill down far enough to get to rock hot enough, how much fluid do they need to flow in order to get enough heat energy to the surface to operate these steam turbines? How big pipes do they need up and down to flow that rate? They also need to flow slow enough at depth to pick up lots of heat, and also fast enough through the mid and shallow depths to not lose all that heat to the local formation before it gets to the surface. For that matter, what's the heat flow rate from the magma into the rock at the depth they were drilling out - how much heat power can we really extract long-term with their setup? (I see jjk166 has addressed that, and that it is another serious issue).
Don't get me wrong, geothermal is a really nice solution, and I wish all the luck in the world to anyone working on using it more. I just don't see any technology here that address the real issues with getting large-scale energy from geothermal.