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?
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.
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.
Welcome to civil court.