Flappy Bird is really an exception to the rule in terms of a popular game that goes viral.
A number of different business models are being tested or used in the video game industry on the mobile side to try to monetize the creations. Advertising is just one of the ways that the companies are finding to recoup their investment. There are many others. In-app purchases is another one. Charging for the game up front is another one. Subscription models are also heavily used in the video game industry. There are many different models, and advertising is just one of those models.