Peertube does not support true "Streaming" that I know of. That's the only real shortfall. If they recently implemented let me know, but I am sure our Peertube instance is at the latest version.
Streams can be done with OBS. I'm doing one now just to add content.
@c1t1z3n0n3 isnt OBS FOSS desktop software to record live streams? What about the server people use to watch it, such as the one you linked to?