This app doesn't have an app.R file - rather, it's split out into ui.R and server.R. You will need to unzip the file and move its contents into a folder which will serve as your working directory. Then, in RStudio, open ui.R and server.R.
Run the library commands at the top of server.R (best way is to uncomment them and send to console). If you get errors, you will need to install the packages that you don't already have. You do this as install.packages(c("packagea", "packageb")) etc. Then recomment them per author instructions.
Once all packages are installed, click the "Run App" button.
That should get you started - the app will launch, but I'm getting errors. It may be because of package conflicts or some other reason which I don't have the time to debug right now. If I have a chance later, I'll come back to this post and see what other help I can give.
Hope this helps get you started!