With all due respect, it's a memory game, not a large-scale web application. I don't understand why "frameworks" are the answer to everything these days. There's nothing wrong with interacting directly with the DOM, especially for something like this.
Speaking of, why in the world does this small front end app need a Laravel back end? Laravel is a full scale framework the size of rails. This is like doing a ToDo MVC app, the pure js one, and requiring Rails.
Especially because, as you were to use something like Angular or Ember, you would just end up implementing the same DOM manipulation code, just wrapped in an Angular directive or whatever
Perhaps framework was the wrong choice of word. I wouldn't call jQuery a framework, but it certainly would have helped. A library like Rivets.js or similar would have been great to see as well, since at that point there'd be (close to?) 0 manual DOM manipulation required (thus obviating the need for jQuery), and he could still keep the page weight easily under 10k.
But what's the point? These days, there's not a whole lot jQuery does that can't be done easily with vanilla JavaScript. Would you rather hire someone who can write lean code with minimal dependencies or someone who throws in whatever library is getting the most buzz "just because"?
I'd rather hire the guy who writes the most maintainable code. jQuery is hardly a "buzz" library, and in this case, using it certainly wouldn't be "just because". It's been the industry-standard method of non-trivial DOM manipulation for years. If he included Angular or Ember or some other nonsense, then I'd be concerned for the exact reasons you stated.