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No, you will not gain infinite turns with this combo.

To break down the interaction:

  • You control a Wormfang Manta (and have already skipped one turn).
  • You cast Animate Dead targeting your Worldgorger Dragon, animate dead resolves and your Worldgrorger's ETB triggers.
  • Worldgorger's ETB exiles all your permanents, including Animate Dead and Wormfang Manta. Wormfang's and Animate Dead's leave the battlefield effects trigger (you can choose the order they go on the stack, I will choose Wormfang on top of Animate Dead).
  • Wormfang's LTB resolves, you gain an extra turn after this one. Turn order is now: You (Current), You (Extra), Opponent, You, Opponent etc.
  • Animate Dead's LTB resolves, you sacrifice Worldgorger Dragon. Worldgorger's LTB triggers.
  • Wormfang Manta and Animate Dead enter the battlefield (you choose the order they go on the stack, I will choose Wormfang on top of Animate Dead). You target Worldgorger with Animate Dead.
  • Wormfang Manta's ETB resolves you skip your next turn. Turn order is now: You (Current), Skipped You (extra), Opponent, You, Opponent etc.
  • Animate Dead resolves, you bring Worldgorgerback and start the whole thing over again.