No, you don't need iTunes in order to be able to use the iPhone Backup Extractor.
The iPhone Backup Extractor will automatically search in the default iTunes backup location for your backups. However, the software doesn't require that iTunes is installed on the computer on which you use it. You can copy your backups to another machine and use the iPhone Backup Extractor there. It is possible to extract on Windows from a backup made under macOS, and vice-versa.
Working with iCloud backups or data does not have any reliance on iTunes.