Zod - you are correct in that assumption. They no longer will sound like THE Iced Earth that recorded SWTWC, Dark Saga, or Burnt Offerings, but musically they remain the same (I hope, judging from those clips). So, in essence, that era of IE's music died when Matt left, just as AC/DC's Bon Scott era trademark died along with him, or Halford-era Priest ended when Ripper joined.
But couldn't you say the same thing retroactively about IE when the other two singers left the band? It's just because Barlow was a member for a longer timeframe that makes it seem so indelible. I would tend to believe that in a few years, IF Ripper stays in the band, that we will be saying the same thing again, should he depart soon after a couple albums.