I've only seen the preview version so someone can correct me if I'm wrong and they included this info later in the segment, but the reason "pinball" (quotes explained in a sec) was largely banned in many cities throughout the US was because 1) It was designed and built for gambling, and 2) the mob had a heavy hand in it.

For about the first 15 years of pinball’s existence, the games didn’t have flippers. All you could do was plunge, nudge and pray, and payouts were the norm. Players could rack up credits on a machine (games back then could rack up 10 – 100 credits or more in a single game) and then “redeem” them at the bar for nickels. A special "knock-off" or "knock-down" switch wiped the credits from the game for the next sucker.

In 1947, flippers were added to pinball and for the next nearly thirty years or so, pinball split into two factions: “skill games” (with flippers) and “gambling games”, which were Bingo games with no flippers. From 1950 to 1960, the vast majority of Bally’s production was Bingo machines, a flipper-less pinball-like game used for gambling, and they continued to produce them into the 1970s.

Check their production history here: http://ipdb.org/search.pl?mfgid=412&yr=1950-1960&sortby=name&searchtype=advanced

Cities and towns often didn’t split hairs over which was which, they simply banned them all, however, in my city of Oakland, the laws were tailored to ban Bingos but not pinball machines. I explained the difference here: http://pinballbayarea.com/2010/12/05/for-amusement-only-strange-pinball-laws-on-the-books-in-oakland/

Pinball-as-gambling was insanely lucrative and naturally the mafia wanted to control and have a piece of the action. Banning pinball was not just a way to "get rid of a moral scourge" but a way to hit the mob square in the pocketbook.

Here's a vid about Bally in the early days:

http://vimeo.com/19585210

edit: not trying to be a killjoy here. The vid is great and well-produced.

Accuracy and comedy and not mutually exclusive.