DevTools: Refactor SettingsScreen implementation.

R=eustas@chromium.org, pfeldman@chromium.org

Review URL: https://codereview.chromium.org/22903007

git-svn-id: svn://svn.chromium.org/blink/trunk@156201 bbb929c8-8fbe-4397-9dbb-9b2b20218538