Hmm never experienced that issue in Firefox or SeaMonkey on Linux. Though normally I would have chat still open when doing max window. One thing you could try is get Livestreamer application and a media player like MPV. With Livestreamer (you do not need to sign into twitch account) search for channel and stream can then be opened in mpv. You can have html5 if you set stream type to hls and put say mpv for videoplayer in livestreamer settings. I found this method can use far less cpu compared to viewing same stream in browser at full screen. If you want chat just open channel chat in a popout with a browser.