Why can´t I transfer app scores from an iPod to an iPhone?

I have an iPod running on iOS 5 and and iPhone running on iOS10. I backed up my iPhone to my computer (Mac OS) using iTunes. I made sure that the apps were on the Mobile Applications folder. I then connected the iPhone to the computer, opened iTunes and found the apps I wanted to install. A “Will Install” notice appeared next to the apps and I synced the iPhone. When the syncing was finished, the apps were installed on the iPhone, but the game progress was lost. Why are the games scored not transfered to the iPhone? Can they be transfered though iCloud?

Any help will be greatly appreciated!