Hi there, josephfrompanacea!
It appears that you have an application that isn't fully downloading to your iPhone on iOS 9. I have games on my personal iPhone as well and enjoy having access to them when I have some free time. I'll be glad to help.
Restart your iPhone, iPad, or iPod touch -- The shutdown and start up process is important to keep the iOS software running properly.
Delete music, movies, apps, books, and other content from your iPhone, iPad, or iPod touch -- Delete the app from your iPhone, then restart your iPhone again. Once your iPhone is back to the home screen, download Hay Day from the App Store.
Let me know how that goes and thanks for using Apple Support Communities!