iPhone 4 App Store won't download apps I'm a user of an iPhone 4 with iOS 7.1.2.  

When I want download an app, it tells me it need to update to iOS 8.4, but it's not supported for the iPhone 4!

Is this only a requirement for specific apps or it is a bug?
If you open the App Store page for an app and scroll to the bottom, there's a section titled "Compatibility" that will tell you what the minimum version of iOS is that the app requires. 

(This is not a screenshot of the OP's problem app, but rather The Infinite Arcade, which was the first app I saw.)