Edit: from the Russian version of the page -
A single drill bit lasted about 4 hours, which was enough to drill between 7 and 10 meters. In comparison, raising and lowering the drilling column took up to 18 hours.
It also mentions that due to the core samples being saturated with hydrogen, they turned to a fine dust unless they were raised very slowly to allow the gas to dissipate.
"It is rumored that at some point the drilling rig began to vibrate unnaturally, as if someone were jerking for it from below. When the well reached a mark of about 12,000 meters, scientific equipment recorded sounds resembling the cries and groans of thousands of martyrs emanating from the depths."
At the scale of a well, the steel drillstring is more like cooked spaghetti. You don't "push" down, you use the weight of fluid (drilling mud) for pressure. The drillstring is only meant to transmit torque. It's easy for it to bend over long distances. (You can even turn things entirely around and use fluid pressure to turn the bit, in which case the drillstring is basically a steel hose that's stored coiled up.)
Is the drilling mud pumped down to create that pressure then, or is it naturally present? Or one pumps water down to turn the grit into a slurry?
As far as how they do it, it's conceptually simple (these days there are "fancier" options with steerable drillbits). You put a tool down the borehole that you can expand and lock in place at the desired depth. When it's expanded, it forms a ramp towards one side of the wellbore. You then lower the drillstring, and when the bit hits the ramp, it's deflected in the direction you want it to go.
After all, if hydrogen is slow to escape from the core sample, it stands to reason it will be slow to escape from the surrounding rock, too.
(Given a bit of electricity, we can easily get lots and lots of hydrogen from water, anyway.)
The rock was more like plastic than rock.