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

To break down the interaction:

 - You control a [mtg:Wormfang Manta] (and have already skipped one turn).
 - You cast [mtg:Animate Dead] targeting your [mtG: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 <strike>You (extra)</strike>, Opponent, You, Opponent etc.** 
 - Animate Dead resolves, you bring Worldgorgerback and start the whole thing over again.