how to get iBooks on Iphone4
As the above comment states, you do not need iOS 10 to download iBooks. However, given the info in your screenshot, it is possible that iBooks is not available in your country.

EDIT: iOS 10 is not out. I have no idea why it would require you have it.

Please review the following article and make sure your device is compatible.

https://support.apple.com/en-us/HT201478

SEE ADDITIONAL EDIT BELOW



I just looked at the App Store, and it DOES appear you need iOS 10!

https://itunes.apple.com/us/app/ibooks/id364709193?mt=8