Which allowBackup attribute is useful to understand if an app can be backup?

I don't know what tool you used for decompiling AndroidManifest.xml but both apktool and Jadx do not show an game_display_name:allowBackup=... entry.

No matter what allowBackup entries you have the only entry that matters is the one in the <application> tag. See Android documentation: https://developer.android.com/guide/topics/manifest/application-element#allowbackup

The other one may be added by the developers because they have not read the documentation carefully.

However the game you are refferring to has a second relevant entry for backup: android:fullBackupContent:

This attribute points to an XML file that contains full backup rules for Auto Backup. These rules determine what files get backed up.

When I look at this XML file I see the following content:

<?xml version="1.0" encoding="utf-8"?>

<full-backup-content>


 <exclude domain="sharedpref" path="appsflyer-data" />

</full-backup-content>

From my understanding of this file format that means that the file(s) in /data/data/com.ironhorsegames.idlewasteland/shared_prefs/appsflyer-data* are excluded from backup.