Yes, people go to Facebook to watch videos.
However, I think it's too restrictive to only consider platforms to be competitors of Youtube only when the use case is analogous, and it's incorrect to imply that Facebook can only be competing with Youtube if their users exclusively use it to watch videos.
Any platform that supports video streaming is potentially competing against Youtube. The specific use case of the platform is irrelevant, only scale and mindshare matter - the degree to which people spend time there rather than on Youtube.