Developer, Ed Kelley, has published MedalBot: an Olympic Medal API for the 2016 Rio Olympics. Kelley developed the API based off a similar API generated for the 2014 Winter Olympic games. The data is scraped from internet sources using import.io, and the entire source code is freely available on GitHub.
MedalBot retrieves gold, silver, bronze, and total medal count by country. The API uses standard GET methods and is read-only. Similar APIs pop up from time to time for single events; and many utilize tools gaining popularity to aggregate data in an efficient manner. For instance, a 2014 API for the Sochi games utilized Kimono, an API creator. Usually, such APIs are free, as they are temporal in nature and simply showcase new technology for current, isolated events.
MedalBot certainly has "side project" written all over it, as you won't find any terms and conditions; but is written using basic API architecture that third parties could use to implement a medal count and demonstrates the power of import.io as a data scraper. Take a look at MedalBot and consider building your own side project that utilizes its functionality.