Are frameworks worth using for small-scale apps?

I've been starting development of a small-scale web application on a single page (or a few) as a hobby project and re-learning some javascript as I go. Looking into the various frameworks and templating languages has been somewhat intimidating however and before I take the plunge into one or some of them I'm wondering if, or to what degree, they would be appropriate for an app of a scale like the one I'm working on. So far I've seen frameworks (sorry if thats not the right term) like express, angular, angular2, react, bootstrap, polymer, ember, and meteor plus other templating frameworks on top of that like jade (pug?), ejs, handlebars, and hogan and also the css pre-processors like less, sass, and stylus. While all these options are great I'm at a little bit of a loss on where to start and which are relevant to a smaller app, if they're worth learning outside of an enterprise environment, and of course which ones to choose.

For a little more detail my planned app is a multiplayer chess game with a main page containing a user sign in, a list of games available to be played and an option to host one, and then the chess game itself on another page. So far I've explored Node.js, NeDB for data storage, Socket.IO for the p2p, and a custom oAuth for the login, but the real-time updating of the match list is something that has me stumped and led me to looking at the frameworks and such in the first place. So, my question is are there any frameworks, templating languages, or pre-processors that are worth learning and using for a small-scale application?