There are multiple ways to distribute your Node.js application…
If you want to put extra work in your project by creating a GUI and distribute your application without having to download Node.JS, I would recommend using Electron. Here is how to use tmi.js with Electron and package / distribute your application on multiple platforms.
If you don’t want to create a GUI but want to package your application into a single .exe file, I would recommend EncloseJS, but it is not free. There are free versions out there doing the same thing (like JXCore), but they are not fully supporting ES6 features yet.
Finally, if you don’t want to package your application, you will have to create a README file with all the steps required to install and run your application. Follow the steps @BarryCarlyon provided and you don’t need to provide your node_modules directory. Since you are going in production with your application, I would recommend installing your packages as exact version dependencies using npm install <package_name> --save --save-exact
Thanks!