And for embarrassment of the original design, the story, and clickbait... they did it on that old machine
They used an Intel Xeon CPU E5-2630v2, it's in the paper. What if in the process of crafting the attack on their old workstation PC they found that it was seemingly possible to do low key sizes very quickly and scaled up from there to a practical attack. Or maybe they have quite the competency in Mathematics and realized their attack was not that computationally expensive.
>Ran on a single core, the appended Magma code breaks the Microsoft SIKE challenges $IKEp182 and $IKEp217 in about 4 minutes and 6 minutes, respectively. A run on the SIKEp434 parameters, previously believed to meet NIST’s quantum security level 1, took about 62 minutes, again on a single core. We also ran the code on random instances of SIKEp503 (level 2), SIKEp610 (level 3) and SIKEp751 (level 5), which took about 2h19m, 8h15m and 20h37m, respectively.
Source: worked with algebra researchers using Magma.
It costs less than a few hundred bucks to do numerous, multi compute AWS server spot instances for cracks on large dictionaries with large hash rates, on random seed password lists (where each password has it's own seed).
If it was trying to crack a quantum-safe where by design the classical computer shouldn't be able to even solve it (except for potentially with a theorem hole) - you'd think they'd start higher.