Prism

It's an awful title and it's calling the guy a spy and a leaker. US, spy and leaker are used as adjectives in that sentence to describe Edward Snowden.
Next time use the whole sentence and not just a "fragment" (US spy leaker) to see what it means, because figuring out that fragment alone is a headache.

EDIT: Also, I don't think you can get "the guy who leaked the fact that the US spies on everyone" from "US spy leaker". For that sentence (US spy leaker) to make any sense, spy must be the noun. But I'm not 100% sure about it. I know @Felicitates; also majors in languages so maybe we can get some help from her. Errr... does she even visit anymore?

Let's see.

"American car manufacturer General Motors ...." GM is not a car, it is a company that manufactures cars.
"American basketball player Larry Bird... " Mr. Bird is not a basketball, he is a person who played basketball.
"American wife beater Bobby Brown..." Mr. Brown is not a wife, he is a person who beat his wife.
by the same token
"American spy leaker Edward Snowden..." Mr. Snowden is not a spy, he is a person who leaks spies.

Now, if it had been "American spy, leaker Ed Snowden" then you'd have a case. But as it stands, and considering the body of the article never once calls him a spy, only using the term "leak", I stand by my interpretation.