That is not it at all. The lawsuit claims (from what I read in the article) that the issue is before turning down an offer to advertise on the site for $300 a month, the company had a 4.5 star rating. Two days after the refusal, the company claims that six out of seven 5 star reviews were removed (by Yelp).
This is about being forced to pay to keep your good reviews, not about page views. The company is just saying that with a reduced rating they saw less traffic, which is to be expected.
Why is Yelp obliged to publish favorable reviews? If a newspaper critic said "I hate this place", that would be fine. But if Yelp does it, it's not fine? Why is that?
1. I have no idea what obligations Yelp has, legally or otherwise.
2. Legal definition of extortion (IANAL):
The use, or the express or implicit threat of the use, of violence or other criminal means to cause harm to person, reputation, or property as a means to obtain property from someone else with his consent.
Seems like (to my untrained and uneducated self) that this would be Yelp damaging the Company's reputation because the Company refused to pay Yelp.
Following the legal definition of extortion, I don't see a case.
It's unethical, certainly, but the action you take against unethical journalists or their publications is to stop reading them. The legal system does not provide a remedy.
This is about being forced to pay to keep your good reviews, not about page views. The company is just saying that with a reduced rating they saw less traffic, which is to be expected.