…It says the card played does not count as a Draw or Play, so does it still end your turn?
A: Yes, while that card you draw from Wormhole (or any of its analogues) doesn’t count against the Draw or Play count as shown on the rule cards, it’s still part of your turn, and the card still counts as being fully played. Whatever it says happens, happens. That’s the risk you take, pulling a card out of the Wormhole! Keep in minds that the turn-ending effect of New Rules is optional, so simply playing them does not end your turn.
Keep in mind you can take the Wormhole option at ANY time during your turn: before your Draws and Plays, in the middle of your Draws, in the middle of your Plays, or after both, if you like. That’s the only control you get to exert: WHEN and WHETHER you decide to play a card from the Wormhole.
Analogues of Wormhole (which is in Star Fluxx) include (some with slight variations such as conditional requirements for use):
Magic Shoes in Oz Fluxx
Shiny! in Firefly Fluxx
There are many other Wormhole analogues in other versions, but those versions don’t also include turn-ending Actions.
See also: Q: What cards have effects that include ending my turn immediately if I play/use them?
See also: Q: What are all the different cards in different versions where you get to draw the top card and play it immediately?