Android Police noted that the feature requires version 13.35.51 to work. You can either try updating the app via Google Play, or grab the installer to sideload from APK Mirror (opt for one of the nodpi versions on that page).
To turn it on, tap your profile icon at the top right of the screen in the YouTube app, then head to Settings > General, and then flipping the switch on the Dark theme option there.
In case you don’t see the option, try closing the app from the list of running apps on your device and restarting YouTube. If it still doesn’t show up, try changing your location to United Kingdom on the same Settings > General screen and then restarting the app.