RL features strictly lateral passing just as RU does, and in my experience this is mostly the bit they don't like. The more I see of American Football the more I realise how little in common it has with any type of rugby, aside from being a sport played by large, powerful athletes and using an oval shaped ball, that's really about it. You could even argue it's more similar to RU with all the stoppages and the specialist nature of the positions/different body types etc.
Well the similarities are running, passing and tackling, basics of RL. The four downs and hand it over aspect has a very close relationship with 6 tackles and hand it over. In fact at one point it was 4 tackles and hand it over.
The restart at the play the ball is much more structured somewhat like the scrimmage in the NFL and nothing like the pig piles they have in RU. Also in RL when a tackle is made we immediately go to a restart as in American football unlike the arm wrestling, pig piling and shoeing that goes on in RU
The specialisation aspect is unique to American football as different teams play offence and defence, not a situation which arises in any form of rugby. The quarterback is a unique position also. Neither of the rugbies has a position where on every offensive play the one man is crucial and handles the ball. The deliberate forward pass is also unique in the NFL and all teams do it whereas only Leeds do it in rugby . There is a form of American football which is mostly used in the college game called the wishbone offence where the quarterback runs with the ball like a scrumhalf and either goes himself or laterals it to a supporting runner of two with dummy runners and the whole bit, quite like some RL plays in my opinion. The forward pass is a minimal part of a wishbone offence so Americans will have some concept of our game, more than they have of RU in my opinion.