- a plugin system
- its custom selector parser (because it had it before querySelector and is not totally compatible with it)
- its abstraction to iron out browser differences (old IE vs standard, notably) that's not relevant anymore
- its own custom (DOM) event management
- its implementation of methods that are now standard (ajax & trim for instance)
I recognize that the DOM API could be better, and comes with friction. Back then, ironing out the browser differences and its selector feature were killer features of jQuery. Today, I do not think the quirks of the DOM API warrant importing a library like jQuery.
¹ but indeed, very lightweight compared to modern frameworks like Angular, React and Vue, with all the ecosystem which comes with each of them (react-router, redux, etc).
If you are going to use many features of jQuery, then it makes sense to use it, but if it's only a matter of writing one or a with wrappers, then jQuery is overkill.
I don't have a strong opinion on the proposal described in the article.