Sorry but that's entirely incorrect. The videogame industry as a whole - both home and arcade - suffered a cataclysmic decline starting in 1983, long before Sega and Nintendo established themselves as console manufacturers here. Read up on the crash of 83; this wiki article is a good start:
http://en.wikipedia.org/wiki/North_American_video_game_crash_of_1983 . Arcades began shutting in droves as people began to perceive videogames as a fad which had run its course. Home machines didn't fare any better, and it wasn't long before the dominant consoles of the day (Colecovision, Intellivision, Atari) were discontinued (Coleco, which only a couple of years early saw huge success with Cabbage Patch Kids, was eventually bankrupted by the failure of their ADAM computer/videogame console). For a couple of years, video games were reduced to a niche industry.
When Nintendo first brought the NES to North America, it got off to a slow start with a lot of people viewing a video game console as somewhat anachronistic. It took a couple of years to take off, but the rest is history. With the success of the NES and subsequent consoles, the focus of video gaming shifted from arcades to consoles. Freed from the business need to suck quarters out of pockets as quickly as possible, games themselves moved from short, fast-paced action titles to longer, drawn-out, more immersive experiences.
So, Nintendo and Sega didn't kill videogames, but resurrected the business. The arcade didn't survive, but it was already on life support by that point.