My apologies, everone -- I just realised that my post may have been confusing, since there is a feature in Youtube called "autoplay", and that is not what I was trying to stop. I was trying to stop Opera from "automatically playing" the video when I visit Youtube. Currently, if you visit a Youtube page with a video on it, the video starts playing immediately, even if you have "click to play" enabled in Opera.
[I think it was fairly clear what I meant if one reads my whole post instead of just the title of my post, but in case it wasn't: I want the "click to play" setting to work as expected, also on Youtube.]
The solution that I found was the extension which forces Youtube to use Flash instead of HTML5. If you force Youtube to use Flash instead of HTML5, then Opera's "click to play" feature works correctly on Youtube.