Q: How can you migrate apps from an old iPod Touch to a new one?

Backup the 4th gen iPod using either iTunes or iCloud. When you get the new iPod you can restore your apps from that backup.

How to back up your devices using iCloud or iTunes - Apple Support

Keep in mind, if the exisitng iPod is running an older iOS, the apps you restore from a backup to the new iPod (which will be running iOS 8.4) may not run on 8.4.

Simple...

-> https://support.apple.com/en-us/HT201269

Apps are not part of a backup.

Only the data is.

If you restore from iCloud backup the latest version of apps will be automatically downloaded. If you restore from iTunes backup the apps and music have to be in the iTunes library since synced media like apps and music are not included in the backup of the iOS device that iTunes makes.

You can redownload most iTunes purchases by:                         

Downloading past purchases from the App Store, iBookstore, and iTunes Store        

You should be backing up your iPod regularly and storing everything on your computer.  Just restore the new iPod from the backup of the old one

Gene Starwind wrote:

 

I KNOW I can recover the apps themselves. That is NOT the question. I need to keep the SAVED GAME DATA so I don't have to start all over again!

Okay.

Then do this  -> https://support.apple.com/en-us/HT201269