yea, the transmuxing is unfortunately buggy though. i had to recently switch my site back to flash because so many browsers have issues with it. it loads way faster though
HLS.js is doing great on Chrome, FF, Edge and Opera. For Safari it's better to use the native HLS player for now.
The best option is to have HLS.js first on compatible latest browsers and Flashls as a fallback on older ones
In case of hls.js used by the NYT, you actually need to transmux the mpeg-ts content used in HLS into fMP4 to make it playable by the Media Source Extensions API used by the browsers.