Why can´t I transfer app scores from an iPod to an iPhone?
Scores are not stored into the app, so the apps backed up into your iTunes doesn't have your scores.

In order to share scores between different devices, I think that developers are usually using iCloud Drive (only available since iOS 8) https://support.apple.com/en-us/HT204230

But older games was using Game Center to share scores, so you will probably be able to share them through this one.
https://www.imore.com/game-center