The Calculist desktop app works just like the web app, except it saves documents on your local hard drive as plain text files. No internet is required. The desktop app works independently of the web app. Eventually, the desktop app will have the capability to optionally sync with the web app, but that functionality has yet to be implemented.
Assuming you have node.js installed,
$ git clone https://github.com/calculist/calculist-desktop.git
$ cd calculist-desktop
$ npm install && npm start