The ball is indeed a different although similar shape.
However, I think it's also to do with body position.
A rugby player should be running towards the opposition line keeping the opposition guessing as to what he's going to do so as to commit his man..
This will come down to body position, ball on 2 hands etc.
To throw the ball out long to the right winger with an NFL style pass, it would require the ball carrier (who is likely right handed) to completely turn his body to the right, so that he's facing where he wants to throw it.
Not only does that take time, and allow the defence to reorganize because they can see where you're aiming, but it leaves the ball carrier hugely exposed to big hits to their side/backs