Of course, for a good user experience, you probably want to do client-side validation of the form; while you can do that a bunch of ways one of the easier ways (from a developer's point of view) is two-way data binding, and I'm using it on a few contact forms, signup forms, file upload forms, etc., scattered around the web for just that purpose.
And if you're doing something more complicated, then you probably want your client side code to respond to user input. If you're using ANY client-side MVC, or if you're getting real time updates from a server (via websockets or whatever), or if you're basically doing any sort of "app" style functionality in the client, you'll probably need two way data binding or its functional equivalent. I've written a big CRM webapp that uses two-way data binding extensively; the old "every click is a full HTTP round trip" model would deliver a shockingly bad user experience.
That being said, two-way data binding isn't the only way to implement rich client-side functionality, it's just one of the conceptually simplest ways of doing it. Backbone has two-way data binding plugins, but the "default" is to use events instead. Ditto for React. But something needs to tie your client side code to user input, and one of the simple "somethings" is two way data binding.
But again, if your app doesn't have any client side code, obviously you don't need anything to tie user input to the code you don't have. So if your app doesn't need any more client-side functionality than, eg, Hacker News has, then you have no need for two-way data binding (or, hell, any JS code at all). But if you want something a bit more interactive, then you need something.
(That being said, I still have no idea what makes this library better than any of the many popular, mature libraries that already exist. I've used Knockout quite a bit; it works well.)