Many, if not most, start-ups don't solve real world problems, and I'd argue that those with the most opportunity capitalize on a consumers want vs. need.
We can start at the top, Twitter, Facebook (contrary to what the article says), Skype, Angry Birds, Little Wings, Pintrest, etc. did not solve a problem. They created something that people wanted.
Basecamp, MailChimp, SalesForce solved problems. You don't have to solve a problem to have a business.