How to offload browser audio links to background player for continued listening.
I have found BSPlayer to be able to play some internet audio streams in the background. 

One unique (?) feature which also I liked is that it has an intent filter for youtube links, i.e. clicking a Youtube link will offer BSPlayer as a choice - unlike the Google's Youtube app, with BSPlayer you can adjust the playback speed - I found it useful for listening to lengthy talk-only videos and presentations where you need to quickly get the gist without wasting too much time.

ps. I'm not affiliated in any way is the app developers.