The reason why Facebook does not have a partner programme like that of Youtube may be that Facebook hasn’t entered the ‘video market’.
Youtube has been the ‘king of the video market’ for the past decade. It had almost no competitive competitor so it was kind of ‘monopolistic’. The users of Facebook were used to share the videos on Youtube on a few tips on the screen instead of posting the videos directly on Facebook. The advertising revenue mostly came from the really short (say 15s) advertisement on the website. They didn’t put much attention on the advertisement before or during the videos (they don’t even have many videos).
In 2015, Facebook claimed that they would start to share the advertising revenue with the video makers to make them more willing to post their videos on Facebook. The sharing format looked very similar to that of Youtube. So it might be the sign of Facebook starting to compete with Youtube and enter the market which was leaded by Youtube. As a result, there may be ‘Facebook Partner Programme’ in the future to encourage users to post their videos on Facebook and attract more advertisement. Who knows?