"There's never been a better time to consider writing your own media server solution from scratch."

If you want to go the hacker route, and do not give a flying fig about UI, you can get a long way just by setting up any old webserver that has range support (which is most of them) and serving out directories with video files and some sort of automated index. You don't even need to do any work. Browsers already are smart enough to hit a video file, extract the playback metadata with range requests and provide native seeking, speed management, and some of the other basics. Plus you get native "right click (or equivalent) -> download" support without anything giving you hassles.

On the one hand, it's missing a lot of features. On the other hand, it can't be beat for simplicity and the bang-for-the-buck is pretty good. And anything capable of A: running an HTTP server at all and B: has enough storage to store the files can saturate whatever network it is on with video data if you want it to.