If you're looking to download the TPE Desktop Web App, well... you can't.
The app truly is a web app and it runs in your browser. Just visit http://app.photoephemeris.com in your browser to get started. If you try to download it via File, Save As... or to save it as a .mht file (Web page archive file format), it will not work.
Make sure you're running a recent version of a major web browser, i.e. updated within the past 6 months, Safari, Chrome, Firefox are preferred.
Make sure your browser is configured to allow Cookies and Local Storage for websites (or at least for *.photoephemeris.com).
If you still have problems, check you don't have some over-zealous security software running that has decided to block access (this happens occasionally).
If you'd like a desktop icon to access the web app, you can usually just drag and drop the address or the web site icon ('favicon') from the browser address bar onto your desktop on most operating systems and browsers.
If you save a link to the web app, be sure to edit it just to read http://app.photoephemeris.com, deleting any of the subsequent parameters. That will ensure the app always opens at the current date and at the location you last visited.