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you know you must not install youtube-dl from the repos?
either clone & regularly pull the github, or just download the executable, and use 'youtube-dl -U' regularly.
It works with the version in MX Linux. You might find an up-to-date version in the Stretch backport. Otherwise try to get the one from MX which should be on Steve Pusser's repository.
MX 17 packages are compatible with Stretch, if they didn't require any extra backports. I make a practice of building them as much as possible in generic Debian environments. In this case, since youtube-dl is a python program and not a compiled binary, it might not make any difference what version you install, though.
admitted, the 404 error could have very different reasons.
but esp. youtube itself tends to change its API so often that the most recent release or even the git master of youtube-dl are a MUST .
it is one of the very few programs where it makes sense to not rely on debian package management (and no harm either). and yt-dl devs make it easy for you, just have a quick look on their website.