"These are new-media ventures that leave the competition scratching their heads because they don't really aim to compete in the first place; their creators are merely taking advantage of the economics of the online medium to do something that they feel good about. They would certainly like to cover their costs and maybe make a buck or two, but really, they're not in it for the money. By purely commercial measures, they are illogical." (New York Times)
Craigslist is a great example of purpose-driven media. They are providing strong competition for newspaper classified ads; however, Craigslist's goal was not to make large amounts of money. It was designed to be a community resource. The New York Times article and Tim's blog both pointed to Firefox as another example of purpose-driven media.
I am not sure that open source software is really purpose-driven "media", since media usually refers to newspapers, magazines, blogs and other sources focused on content. A more appropriate term might be "purpose-driven technology" referring more to the method of creation (open source software) rather than a media outlet.
Open source software fits well within the Christensen disruptive innovation model by approaching the market in a very different way to fill a niche need along the edge of the market, but then grows to displace the mainstream market. This idea ties into the purpose-driven technology concept for open source software especially well when you consider the origin of many open source software projects and how they began to fill their niche market. Linux started when Linus Torvalds wanted a Unix-like system that ran on less expensive hardware for his own use. Linus did not start this project to make money or disrupt an industry; however, the end result was purpose-driven technology that may have seemed like an illogical competitor for Microsoft and Unix operating systems from an economic perspective. Many other open source software products had similar beginnings and a similar purpose-driven technology as a result.