Your media keys should work without the browser window active for Chrome and Opera. Firefox only supports the play/pause key and only if the browser window is active. You can however change the key assignments for this extension, to any key combination that you'd like, by using the shortcuts manager for the browser.
Supported Sites: youtube, pandora, spotify, bandcamp, google play, yandex, soundcloud, tidal, deezer, plex, vk, subsonic, jamstash, overcast.fm, music.amazon.co.uk, music.amazon.com, di.fm, netflix.com, and tunein.com.
Please find us on GitHub if you'd like to request features, post issues or contribute to the project.