You put the backup on your new phone by setting the new phone up, signing in to the iCloud account that the backup is on when prompted, and then selecting "iCloud Backup" when you get to the screen that asks you how you want to set the device up.
You do this via Wifi, not via iTunes.
Your screenshot very clearly shows that an iCloud backup was done for the iPhone Gold device yesterday.
Not sure what it is you are looking for beyond that?
GB
And just an FYI - you can see your iOS Backups to iCloud on your Mac by clicking on the in the top left-hand corner of the Mac, then clicking on System Preferences>iCloud icon>and at the bottom right of that screen clicking on Manage, then Backups: