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 Worldgorger back and start the whole thing over again.
So you can continuously flicker the Worldgorger with animate dead, but each time Wormfang Manta enters the battlefield it makes you skip the extra turn that you got when it left.
If you are looking for some infinite turns with Wormfang Manta, perhaps try something with Torpor Orb and something to flicker your Wormfang like Eldrazi Displacer?