This "machine [that] perform[s] those steps" sounds exactly like it is a static site generator.

Yes, that is the intended meaning. This static site generator is non-traditional; it should live as first-class content on one of the pages of the site it outputs. This is not the way traditional static site generators work, although they should.

Sounds like a fucking weird place to keep it, so I don't think they should.

Not weird to suggest that an organization's website should serve as that organization's knowledge repository. Weird is the tradition of building out websites that are little more than Potemkin villages for the entity they represent. A Engelbart-style DKR <https://www.dougengelbart.org/content/view/190/> is certainly not bizarre as willingly participating in the inconvenience of relying on out-of-band documentation like a README that exists only in the source repository that lives on, say, GitHub, and a set of scripts/binaries that you have to download/install/configure separately and whose esoteric conventions you will have forgotten by the next time you try to update the site a year and a half later <https://corytheboyd.com/posts/2020-03-09>—or worse, you find those tools no longer work, even though you do remember how to use them.