What do you mean you're not using their API? If you're screen scraping the content, you're still violating their terms of service.
"You also agree not to, and will not assist, encourage, or enable others to:"
"Use any robot, spider, site search/retrieval application, or other automated device, process or means to access, retrieve, scrape, or index any portion of the Site or any Site Content;"
"You also agree not to, and will not assist, encourage, or enable others to:"
"Use any robot, spider, site search/retrieval application, or other automated device, process or means to access, retrieve, scrape, or index any portion of the Site or any Site Content;"
https://www.yelp.com/static?country=US&p=tos