The primary reason to make YoutubeSearch a class is, in the future, implementing searching other video sites and taking advantage of inheritance in the implementation. That isn't demonstrated here, but the plumbing of "doing a request", "providing an iterator" and such could be promoted to the base class and subclasses are only responsible for knowing their domain.
Having YoutubeSearch be a class doesn't really bother me, especially since the point of the post was to demonstrate the use of __ methods, and you can't do that if you're using a method instead.
However, I discourage promoting inheritance (except in the guise of mixin, and even then...) as a way to factorize common functionalities. Composition is usually much better suited.
