What particular sources of video with DD 5.1 audio do you want to stream via a browser rather than a dedicated app?

I'm just trying to understand what your intended use is, given the big VOD services provide their own app, which negates the need to use a browser. Of course, some of these services don't provide DD 5.1 - here's looking at YouTube, Lightbox, Neon... - but Netflix and Prime, for example, are in DD.

If it's 'alternative' streaming sites you want to use, perhaps download the content via other 'alternative' means and use Kodi (or VLC) to play the files (provided you can sort them out for 5.1 - I'm not sure if you're having problems playing 5.1 on ALL content via Kodi and VLC including downloaded files, or simply streamed content).

IME browser playback will only work with discreet channel outputs, not for taking a pre-encoded DD stream and sending out out without changing it. Makes sense since  you would want to mix browser in with other stuff. Even then I cant recall the last time I had anything from the rears from a browser other than some wired demo site showing how it could be used.

Apps like the netflix ones will take control of the audio output and block all other playback when in use, so they can just dump their audio output over the digital output. 

I'm not actually bothered about this, just trying to understand it better. It started as idle curiosity, not a need or desire to stream any particular site. I saw some links, mostly on YouTube, that said they were DD 5.1. But when I tried to stream them with a browser, I only got stereo. So I started wondering why that was. And then as I looked into it further, I encountered this enormous rat's nest of confusion about whether DD 5.1 can be streamed at all with a browser. I'm not bothered if it can't be, but the confusion and contradictory information is annoying, especially if you don't already know a lot about this kind of thing. For ordinary users who don't know a lot, it can be enormously confusing. Why should this be so? 

Having started this thread, I decided to see if I could find some definitive answers that might be helpful to others who were feeling the same confusion. So I did some tests and have now reported my results. People can do with them what they like.

I have apps for some sites but for a lot of the sites that interest me, there either are no apps I can find, or the ones that exist only work properly with phones and are not suitable for the Shield. So I use a browser to stream those via HTTP. 

I have no problem playing DD 5.1 via Kodi from a file. The issue I was trying to answer was whether this was possible with streaming from a browser. Apparently it is not.  

Remember that optical/coax are quite poor ways of achieving surround sound, despite people continuing to recommend them over HDMI based on outdated knowledge. They can only pass through a pre-compressed surround sound signal, and only basic DD 5.1 at that. They do not have the bandwidth to pass through decompressed/PCM/discrete surround tracks. If your video player is decoding the compressed audio rather than passing it through, you will not get surround sound over optical. If your test file uses compression any more complex than DD 5.1, you will not get surround sound over optical. If your test file uses an audio track with discrete channels (usually MP3/AAC/PCM), you will not get surround sound over optical (unless you use something clever like Kodi which is capable of transcoding any original audio track into an optical-friendly surround format).

As rich said, your browser is decoding the DD 5.1 files and attempting to send the resulting multichannel PCM to your receiver. This is standard behaviour for any non-dedicated media player software, because bitstreaming a compressed signal means that the operating system can't mix the audio or otherwise touch the signal in any way. In other words, to get the playback behaviour we expect from a computer (like being able to hear system sounds/other browser tabs while playing a movie), the source signal has to be decoded to raw/PCM first. As optical doesn't support 5.1 PCM, you're getting 2.0 instead. If your receiver was connected with HDMI, you would get 5.1 multichannel from your browser.

Kodi, as a dedicated media player, bitstreams the untouched compressed DD 5.1 signal and you get 5.1 playback with your current equipment.