It's best not to think of it as being a standalone application, like ms-word etc. Shiny "apps" require R to be running, so they are not standalone. The interaction is carried out with a web browser, and your snapshot shows that you are trying to use a temporary, local browser "URL" that is created temporarily to show the R output.
If you want to run the shiny app locally, you need to use R to load up the R source file. Many people use RStudio for that, but other ways of obtaining R will also work. They generally provide the user interface via a browser, and will open up a browser window pointed at a temporary "URL" when you launch the app.
The R-shiny system is not akin to a windows (or mac or linux) "app". In windows/mac/linux, you can create a compiled object that can be invoked by you or shared with others, and run by clicking something in a UI or by typing a command. And then, that app will interact with the GUI system to produce output and seek input. This is not how shiny works.
PS. shiny is available in other languages as well, not just in R. But they all share this property that the UI work is done via a browser. The shiny system hooks up code (in R, python, etc) with javascript code that interfaces with the browser.