Well, to be blunt: You're doing it wrong!

If you want to be able to rebuild your server from scratch, you need a backup of this server's master database, not one from a different server.

The exact contents of master is unique per instance and yes, it contains information (including file paths) on all other databases on your instance. Hence, if your instance is somehow screwed up, but the file system is still intact, you can often get away with restoring only master and your SQL Server will automatically sort out everything else on first startup.