A user who wants to publish a video could do that in the form of special links which contain a hash of the video (maybe magnet links do that?).
They could do that on their own website for example. Or in multiple places. Their website, their GitHub pages, their Twitter etc.
The viewer (say Joe) who wants to see such a video would click the special link and have a software that searches it on a decentralized network of nodes.
Some other viewer (say Paul) who recently viewed the video and still has it in his cache could deliver the video to Joe.
In return, Joe could automatically get some crypto currency. Say worth $0.01 or so.
Content aggregators could crawl all these sites and create an experience similar to YouTube. Or maybe this could also be implemented in a decentralized fashion.