Is English your first language? I'm not asking out of disrespect. I'm genuinely curious. The grammar of headlines and titling is often confusing to several non-native speakers. Incomplete sentences and 'news speak' play a vital role in language. For starters, it isn't a mouthful.

http://esl.about.com/od/intermediatereading/a/newsheadlines....

If you want a complete sentence that's more aligned with the meaning and intent of the original headline, try the following. "[A|This] Middle-School Dropout [Codes|Coded|Is Coding] [A] Chat Program That Foils NSA Spying." The one you wrote has some subtle, imperative differences in meaning. Adding "[the ability of the]" is hypercorrective. And it's verbose. "NSA Spying" is appositive speech; it's perfectly normal and understood.

What's not clear about the title in the first place?