Play out, like a game that is not particularly exciting. It "plays out" naturally to the end. You could imagine an ordinary life "plays out" without drama. Headlines capture attention. So they "scream". It's a fairly common idiom in English.

She is saying she is interested in the people that don't typically make the news or famous people. The "scream of headlines" would be the famous people in the news, and she wants to know the lives that happen elsewhere.