The "Download Now" link directs you to the iTunes App Store, where you must continue the download process. You must have iTunes installed in order to open the link, and you must have an active iTunes account to download the application. This download may not be available in some countries.
AsteriskCLI allows you to connect to your asterisk through SSH and perform any command on it, right from your iPhone. The only configuration you need to do is to allow access through SSH to your Asterisk server.