When I said init in the above I meant it generically, referring to the code you posted as initializing an instance of the owl slider. However, it is a popular function name used by many plugin authors and also by coders in general. It's not a required function, although again, almost all scripts, other than the most simplistic, have some sort of initialization or setup. But as I say, the person writing the code doesn't have to use the name init. And if they do, it might be used for an internal function, not necessarily for what I was referring to as an init.

So in the sense I was using it, I would say most plugins and scripts in general do have an init. A few simply look for something specific on the page and act on that if found. Even those often have an optional init if you want to fine tune what they do.