I’d also mention here that the 1-extra-point method is very easy (for football players, at least) and almost always chosen, so in practice, a touchdown can usually be thought of as being worth 7 points.
But yeah, that’s a pretty good starter explanation, overall. More details would surely emerge during the game, like the different ways to move the ball.
Just as an aside, an explanation i recently heard of the difference between American football and Soccer:
American football is a game for coaches, soccer is a game for players.