Football without blocking or tackling is a completely different game. Might just as well just play soccer or ultimate. Which, in fact, people do.
Those who want to poke maximum fun at couch potatoes always seem to pick American football for their examples. That's because civilians don't actually play American football, so there's relatively little danger of an embarrassing counterexample popping up. (Actually, plenty of teenagers play American football, but perhaps teenagers know better than to try to argue with curmudgeonly trolls on the Internet.) It's rarer to hear people try to make fun of Americans for not playing basketball or, god help us, golf... because in any city in America a golf course or a pickup basketball game is probably no more than ten minutes away. I know a bunch of middle-aged adults who play basketball. I know this because they occasionally turn up with basketball injuries. ;)
Incidentally, I only just noticed an incredible folly at the heart of this article: If you sample teenagers, you'll find a much larger percentage of them playing sports. But a smaller and smaller percentage of the American population is under 25. Is it really such a terrible thing that so few 55-year-olds play contact sports? Aren't our emergency rooms busy enough as it is?
Rugby is also a terrible sport to play casually with high impact tackling.
When you think about it even more casually, going down to the park with a few friends, rugby and american football are both hard to replicate. Sure you could pretend to both be quarterbacks and pass the ball back and forward but it's really nothing like the actual sport. Same with rugby which is mostly backwards passes.
Taking the American sports angle you can see why it's much more common to seeing friends playing basketball casually as getting a few friends together you can mostly replicate the game.
Most major american cities have one or more rugby clubs. It is great way to unwind after a long day at the office. You should definitely have good health insurance, and be prepared to accept some longer term consequences, but unlike football, there is a fairly active (albeit small) adult population that engages in the sport.