Am I missing something? Surely...
However, as noted in the article and by yourself, real life is never so constricting as only allowing you one chance at any particular person.
On the other hand, once you've passed on someone, there's nothing to guarantee that you'll be able to go back (they could be engaged, have moved away, hate your guts for evaluating mates by a mathematical formula, etc).
Well, you can't guarantee you choose the best, but you can try to maximize the chance of doing better than random.
This models real-world situations such as (the article example) picking a wife from a pool of women, or even something such as who to hire from a pool of job applicants. In these scenarios, job candidate you passed on might take a different job, or the woman you choose to marry means you can't date the rest, or vice versa.
Obviously, if you can examine everyone and then go back and choose, you'd do that.
The irony is Kepler actually did get to go back - he hesitated on #5, she became unavailable, then he went through the rest of his list of women... and went back to re-woo #5. So he got to see all the candidates before choosing. ;)
This algorithm seems optimized towards getting near-optimum rather then limiting risk. I think for real world problems it'd be much better to lower your standards as you near the end of the pool.
You can unknowingly happen to choose the second best if the best candidate occurs among those you never consider because the second best is the best 'so far' when you get to them.
But the way it's described in the article is incorrect, as far as I can tell.