It's always bothered me to no end that PG has his essays read by others prior to posting. This isn't academia (or an application to college or a job application) and he's not writing for a journal and requiring peer review (or comments or suggestions). Fine it's his own style apparently.
Now what would be very interesting is to see some of the reply comments on the drafts of the PG essays (and how extensive they are).
Whatever the "it" is that constitutes a startup's purpose often can't be fully articulated in mission statements, OKRs, core values, etc. Either it's simply ineffable, or it's a metamorphosizing snapshot of the leading edge of a rapid process of discovery. Expecting such an already-abstruse concept to faithfully percolate down a rigid reporting chain is ridiculous, like sending old-English scrolls via carrier pigeon to narrate a live sporting event.
But communication of the "it" still has to happen, if imperfectly. So someone in founder mode would naturally focus on delivering the most faithful and timely version of "it" to the points in the organization where it'll have the most impact and be least susceptible to corruption in transit. Today that might be to a UX engineer. Tomorrow it might be to the board. It's a kind of plate-spinning that aims to reduce skew from the latest version.
I don't know -- I've never worked at a strongly founder-driven company. I'm just trying to figure out what the essay means.
But in general I think it's clear: founder mode here means having strong opinions about all parts of the company. Maybe it's a technical founder telling salespeople what they should emphasise in their sales pitches, or a nontechnical founder giving directions on choice of technical architecture. (And I think either of those examples would provoke different reactions in most people here).