The issue is that they forced a buffer to overflow--they put N bytes of data into a bucket that was can only hold n bytes. The extra N-n bytes were carefully chosen so that they would do something "interesting" when they spill out of the bucket and into the program's code (there are ways of avoiding this, like the No-eXcecute bit, which I guess were ignored/turned off for this demo).

In some ways, this is easier to do with unstructured data. If there was some specific format, the overflowed data would have to fit into that format AND do something malicious.