It is fraud, there should be no mistaking that. If you take someone's money with absolutely no intention of fulfilling the service or product they're purchasing, it is fraud, period.
It doesn't take a technical founder to log in to Stripe and shut down the payment processing. Or to call Stripe and get it turned off. It doesn't take a technical founder to alter the settings on the domain name and blank it that way either. I know people that can barely use email that can change settings on a domain.
It might cost $200 to $500 - worst case scenario - to hire someone to take down the consumer facing part of the site (or plainly neuter it). More than likely they could reach out to any number of contacts and get it down for a lot less than that. Don't have a few hundred dollars? Well then your responsibility is to go crawling to your family, your friends, Techstars, whomever to get it. Just to save their reputation, I'd be willing to bet Techstars would have helped in getting this shut down had they been asked.
There is no excuse for what they've done.
Being too lazy to shut off the site is not an excuse.
You cite the failure mode of startups as a "fact of life" with regards to two particulars, and minimize the ethical responsibility of the hypothetical non-technical CEO on the basis of implied incompetence and his or her technical inability to do anything about the situation due to both his or her failure to plan for the eventuality and the actions that he or she has just taken. That leaves you with two "that's just how it is" statements and one "what can I [he] do about it anyways" statement, lined up against one "could this have been handled better? Yeah" statement. I believe you might agree that that looks like a pretty weak argument, on a second read; if not, I'm certainly interested in what you have to say about it.
If you're the non-technical CEO of a subscription commerce company in this situation, did you mean to do anything wrong? Of course not, no-one is going to assume that. Does that mean you aren't to blame and it's not your fault and you're not responsible for the situation because who knew startups were high-risk and computers are hard? In the scenario you outline, it would not give me confidence in a person to hear that he or she believed such a thing.
More notably, though, and perhaps interestingly, the author mentions that it does not give her any particular confidence in "Techstar" as a brand. Interesting because of the implicit assumption that the VC incubators are effectively vouching for the reliability of the startup and assuming a degree of governance / diligence with regards to the potential extremes of the outcome, which in turn raises the question of whether that's an idea that the incubators are selling (perhaps unwittingly) to their prospective investments. So, I think something like that might be more productive to talk about than situational ethics, really. But I didn't want to leave you with the mistaken belief that everyone had come to the same conclusions about the facts of life.
You also have very limited options for avoiding liability for fraud. I don't think using the excuse that you were a non-technical CEO is one of them.
Startups fail. Fact of life. We talk about "burn rate" and "runway" because it is easier to say than "The number of days you have to find a working business model or secure additional investment, after which you have to fire all of your employees because you cannot make payroll."
When startups know they're going to fail to make payroll, they fire all employees. Fact of life. Fired employees are the worst affected people when a startup collapses, by a factor of lots. They don't get to call up their credit card company and chargeback forgone wages for the last three years.
When you're the non-technical CEO of a subscription commerce company, and you find yourself in an empty office without employees, if you're hypothetically aware that subscriptions are still active -- which you very well might not be aware of -- you have very limited options for actually fixing it. You might as well ask my dad to do an orderly shutdown of Appointment Reminder given I get hit with a bus tomorrow.
Could this have been handled better? Yeah. There's a reason that when startups ask for advice on what to do in their remaining hours of life we always say the words "Prepare and execute on a plan to effect an orderly wind-down of the business." It's not exactly something people are born knowing and might not be at top-of-mind while they're going through an enormously stressful event.