This is because Atticus is a Progressive Web App (PWA) the installation process is a bit different to standard programs. First, because the program is operated through your browser, you'll need to use a browser that supports PWAs. Chrome offers the most robust support for Progressive Web Apps, and will allow you to download Atticus and use it as an app.
On some systems, the icon in the browser bar will also work better than the icon in the Atticus interface. You can see where to find this icon in the browser bar in this tutorial: https://www.atticus.io/accessing-atticus/
If you are using Google Chrome, you may want to check to make sure that the App hasn't already been installed automatically. You can see your Chrome apps by typing chrome://apps/ into your browser bar. If Atticus is already present here, you may just need to right click and create a new shortcut to the app so that it appears on your desktop.