Just because it's algorithmic doesn't mean it's legal or clean. I can write an algorithm that searches your cookies for porn sites, figures out who employs you, and emails you a customized extortion threat. If their algorithm works the way it's described in the article, then it'll downrank or remove 10 legitimate, positive posts from real customers if they're made in one day, and will preserve and uprank 1 illegitimate negative post from a competitor, unless the unwilling subject of this debate agrees to pay to remove the negative review. That's the definition of extortion, and if ever there was an algorithm written for that purpose, the one described in the article is it.
The way I understand this is, that he was not asked to pay to have the negative review removed, just for advertising, which was totally unrelated to his reviews.
He was asked to pay for advertising. He wasn't happy with previous dealings with yelp, so he declined. Then, all of the positive reviews that were on the site mysteriously disappeared. One plausible explanation is that all of the positive reviewers removed their responses. Another one is that all of the positive reviewers weren't real. But a third explanation is that they were removed precisely because he chose not to pay for advertising. And in the business owner's mind, that is what happened.
If there was a reasonable or non-negligible possibility that removal of the positive reviews resulted from his failure to pay the bribe, then the onus is on the company to provide records to the contrary. That's the point of subpoenaing the poster of the negative comment that survived; not to sue him directly, but to establish the mechanics of and facts arising from Yelp's algorithm, and to establish a pattern of extortion.
Consider: Yelp's algorithm could just as easily flag EVERYONE who gets a single star review for a sales phone call.