A proof is not like a program. The goal of a program is to "do the thing", thus you can make the argument that it doesn't matter what the code looks like as long as its works right. But the goal of a proof isn't to "do the thing" (where "the thing" is just to print Yes or No), it's to communicate. An unintelligible proof is really just a first draft.

its important to read it anyway because there have been and will continue to be errors in the construction of the proof software itself. which leads ai and humans alike to prove things that arent true

i think they're talking about the writeup