Per [1], “[wells] with a regular production casing diameter of 200-250 mm have an average capacity of 5.5 MWe”. Quaise has deep bores that could potentially have higher temperatures, but let's stick with 5 MWe.
At the article's 12 MWh/m³ for drilling, and 250mm bores of depth 10km, WolframAlpha tells me that is 6 GWh.
Divide through, you get 1000 hours or about a month. This doesn't match their “significantly over 10 years” they gave before mentioning waveguide losses.
The main difference I suppose is the thermal conductivity comment, where I didn't follow why Quaise wouldn't be able to use enhanced geothermal approaches. More specifically I think that if a Quaise well has ~1% the energy output of a normal geothermal well, it's pretty weird to frame the problem as about the energy cost of drilling, and not the whole factor-100 reduction in energy output.
To be clear, this seemed like an interesting article and I'm not claiming my napkin math is definitive, I really am neither an expert nor someone who has spent a lot of time investigating this. I do think some more clarity on how the math looks would help their case.
[1] https://www.thinkgeoenergy.com/report-success-of-high-temper...