This is probably in reference to several major US municipalities that banned pinball in the mid 20th century.
Often this was because gambling machines were starting to disguise themselves as pinball machines to skirt around anti-gambling laws. However, in at least one case in New York City, pinball itself was purposely banned for about 30 years, because Mayor La Guardia thought the machines were ripping off kids.
The pinball industry got Manhattan courts to overturn the ban in 1976(PDF) when the court found there to be an actual element of skill to the games. Chicago and most other major cities followed in rescinding their bans. However, it looks likely (wasn't able to verify this to my satisfaction) it is still illegal to play pinball in Ocean City, New Jersey on Sundays.
I realize that pinball (usually) is not a "video game". However, "arcade" video games as we know them did not start to appear until the early 1970's and were likely in the same skill/chance boat as pinball in cities that banned pinball. The history of the medium does show an explosion of new games starting in 1976. It's tough to discredit the possibility that the fall of the pinball game bans in the same year might not be entirely unrelated to that.