Has Windows Server Backup's Disk Space Management Changed in Server 2012?

That article you link is wrong. There is no way to specify the retention policy in Windows Server 2012 when backing up to external disks. I don't know why they lie like that... The configurable retention policy feature DOES, exist for the Windows Online Backup feature that you can use in Server 2012. Possibly this is where the confusion arises.

AFAIK backup disk space usage is the same in 2012 as in 2008 R2, which was also supposed to handle retention automatically, but didn't always work. When this occurred in 2008 R2 we would use the Diskshadow utility to manually trim VSS versions from the backup disk, which is what I'd advise you do here.

Use diskshadow to delete oldest VSS copy from Windows Server backup disk: http://www.bluecompute.co.uk/blogposts/windows-server-backup-manually-delete-snapshots/

EDIT: As Twisty points out, Diskshadow is not needed for this any more, you can use the new WBADMIN DELETE BACKUPS command