This sort of thing comes under the heading of what I would call "being an asshole". Every example of this kind of argument looks like someone trying to make themselves look superior and humiliate the other person. It's really yucky. Thanks for pointing it out as a specific case though, I'm going to start noticing this tactic everywhere now!
This seems related to (though not quite the same as) "Eulering".
A remark about your startup founder / investor example: I think most startup founders meeting with investors absolutely will have concrete answers to questions like "where will your business be in two years' time?" cached in their heads, because that's the sort of thing investors are likely to ask about. So I don't think I agree with "Most founders aren't going to have committed projections of those specific dates to memory even if they do have a coherent business plan" in this context: I think they likely will have, at least if their coherent business plan is one that supports such projections and the projections are positive-sounding enough to share with a prospective investor.
(I think a well prepared founder will answer the interruption with something along the lines of "That's slide three, which we'll get to in a moment. Now, as I was saying, ...".)
Do you consider Evidence-based Medicine generally to be an argument by intellectual ordeal? (BANG energy drinks would be a medical intervention in this case)
I do agree, and I think relation to information and authority are forged in real world, where sometimes, the bottom line is based on might makes right.
Unfortunately kids are often right, but parents have higher agency.
The same goes for teachers.
So is it really that surprising we are a world of adults who aim to have higher agency than the other person?
We have been taught that authority stems mostly from force, not smarts.
By agency I mean you overpower the person, but not cooperate.
A general does not have to be paradoxically smarter than ordinary soldier in order to be a good general.
Someone running a business does not have to be smarter than the guy who does the work for the person running the business.
However we are taught otherwise.
Is the President the intelligence hub of the world? Hardly? Then why bother right?
The other problems are that debates with adversarial people may not be fun or good ethic, but they do supply people with hard to knock out arguments.
Or to quote some guy "Anger does not solve anything, but it does provide good arguments."
Second line of though would be even more important.
Two people can be both wrong and right at the same time.
Two people can be both wrong.
Two people can be both right.
Sometimes a debate might end like two swordsmen who impale each other.
I also think that many good debates should be done at least twice at different times.
As long as something is that important, the idea of doing the same debate twice gives both parties time to digest information.
We know from psychology that brains integrate and digest information over time periods, where the mind is inactive. This makes the brain able to filter the effect of outside input and thus your mind can sort things without being disturbed. Like in sleep.
However usually that is not goal of debate.
There once was an extremely annoying child named Jacob. One time during recess, Jacob decided to take up the entire playground bench by lying down on it horizontally. A classmate came up to him and said something like: "You're taking up the whole bench! That's not fair!" Jacob responded: "Ugh, you people don't know what I'm doing! Do you even know what quarks are?!" The classmate said "umm..." thoughtfully for a few seconds, and then scuttled off.
While an effective rhetorical technique, knowledge of the existence of quarks was not a very relevant indicator for who was right. The question didn't test for knowledge relevant to playground bench allocation problems, didn't correlate well with even general thinkoomph, and neither of these would've correlated well with correctness in the first place because of Jacob's clear conflicts of interest.
Medieval Europe had a method of determining guilt called "trial by ordeal". If two parties had a large dispute - say one accusing another of a serious crime - they would sometimes decide who was right by fighting to the death in an arena, or having the accused willingly ingest poison and see if they threw it up instead of getting sick or dying. The presumption was that God would favor the one telling the truth, or maybe that their skill would be bolstered by their sense of righteousness.
I like to pejoratively call the type of fallacious impromptu challenge-giving I just described "argument by intellectual ordeal". The lifecycle of the rhetorical tactic goes like this:
Like "arguments from authority", the "argument by intellectual ordeal" comes with standard justifications that are almost always overused. In the case of the "argument from authority", the surface justification is something like "People with the X rubber stamp tend to be very good at answering these questions, so it's only natural that we defer to their expertise even if we think we have a gears-level model that says they're wrong." Much of Inadequate Equilibria is a long case study as to how, on deeper inspection, appeals to expertise can be a smokescreen for a more pernicious and instinctual aversion to Intellectual Immodesty, and not really predicated on that authority's incentives & track record.
When it comes to "argument from intellectual ordeal", the surface justification given by proposers is usually that succeeding at the challenge would either suggest some domain-specific competence or knowledge, or highlight the consistency & predictive power of the other person's world model. The pernicious underlying rationale, is that when someone is unable to respond to any surface-relevant challenge or inquiry raised by interlocutors, that seems enough to make one 'lose hit points' in a debate, whether or not the challenge tested something meaningful in the first place.
I think most people would agree that the examples I've shown so far are silly, and it'd be a social faux pas to make the demands to adults. Most real world examples of argument by intellectual ordeal however aren't quite so clear cut, because they're either more directly relevant to the topic or are embedded in more innocuous lines of questioning. Often it's just the way a critique is phrased into a question that turns it into a challenge and not an argument. Let me show you some examples I've been involved in or witnessed, and explain why I think there were better alternatives. Note that I'm not taking a stand here on the debates, just noting the tactic as present:
Sometimes, very rarely, appeals to authority guided by a correct notion of market efficiency can be useful. I don't think I've ever encountered a situation where "argument by intellectual ordeal" was the best available option, in practice, except when the person's aptitudes were the explicitly acknowledged and unanimously accepted topic of conversation. So I have two pieces of advice for potential interlocutors. First, if it seems like someone has "challenged" you during an argument, don't just lean into the challenge reflexively unless you're absolutely sure you can win it; take a few extra seconds to make sure the challenge is relevant and then state your objections if you have them. If you do attempt the challenge and fail, it will be harder for you to claim later that the exercise was meaningless even if that's true.
Second, try to keep conversations conversational. Ask people questions primarily to understand their ideas and pass their Intellectual Turing Test, not to win a game of anticipating some hard-to-see consequence of their map (unless respectfully examining their ability to do that is actually your primary goal). If you have objections, state those explicitly and then give examples of arguments that would change your beliefs, instead of unilaterally demanding responses of a certain kind.
In hindsight, the fact that the question was delivered this adversarially may have been deliberate. As I later realized while reading Elder Rationalist Zvi's posts, one alternative explanation is that it was testing presentational skills useful for impressing pseudo-incompetent downstream investors. In this case the question might have been much more plausibly relevant than it would first appear.