I don't know if it applies to the web server, but for the command-line version of youtube-dl, it has a -U option that updates itself. One could create a batch file or shell script that runs that each time, before downloading a video, or do it manually once in a while. Like someone else said, I think the creator updates the app fairly often.
Edit: I had written a post about youtube-dl describing its use a bit, and also a quick look at its code: