Twitch is one of the popular sites that don't have a working HTML5 player for the masses (it does work without Flash using the methods above). There's Beam.pro which has some interesting approaches to live streaming with HTML5 [2]. The only thing I haven't found a great solution for are the big Music streaming sites, which all rely on Flash (the others shut down). Some people told me Google Play Music may or may not work with HTML5 but I haven't tried that yet.
Also, a great number of websites will ask you to turn on Flash when installed but deactivated and only use the HTML5 player when it's not actually installed. I guess it's a design flaw that Browsers report disabled or click-to-play plugins to websites.
0: http://rg3.github.io/youtube-dl/
1: http://docs.livestreamer.io/
2: https://forums.beam.pro/topic/168/where-we-re-at-with-html5-...