I've been using this chrome extension [1] and actually forgot they removed the dislike button.
[1]: https://chrome.google.com/webstore/detail/return-youtube-dis...
[1]: https://chrome.google.com/webstore/detail/return-youtube-dis...
From the FAQ
> Where does the extension get its data?
> A combination of archived data from before the offical YouTube dislike API shut down, and extrapolated extension user behavior.
New videos will only show dislikes sent by people using the extension. There's no way to know the real number anymore.