It began airing in the '70s. It was initially called Wide World Wrestling before they switched it to World Wide to supposedly prevent confusion with Wide World of Sports.
 
One of my earliest memories from the show was was when I first started watching JCP in 1987. Hiro Matsuda choked out Johnny Weaver and caused him to bleed from the mouth. It was part of the build-up to the Luger-Dusty match at Starrcade '87. Weaver had taught Dusty the "Weaverlock" and was going to be the "keeper of the key" for the cage.  
 
Other memories include seeing some matches from Bash '87 like Flair beating Jimmy Garvin in the cage to get his dream date with Precious and the match where Ronnie Garvin won the title from Flair, which took up the whole hour.
 
I also enjoyed some of the stuff WCW was doing on the show before they signed Hogan in 1994. They had "May Mayhem" month where they had a specially stipulated dream match every week like Rude vs. Sting in an I Quit match and Austin vs. Johnny B. Badd in a Tuxedo match, and they also had the "Marquis of Queensbury" series between Flair and Regal.

My first vivid memory was tuning into the old World Wide Saturday night show (11:30 pm) to hear Bob Caudle announce the tragic accident that befell Magnum T.A.  I had just started watching wrestling in the weeks prior, and had seen Magnum's matches with Nikita, Flair, and Tully, and was hooked for life. When Magnum got hurt, it was so shocking.... Miss the old NWA days.

I think the Youtube clip you have reference to is from the old WGHP channel 8 studio from 1974 It's also on the Mid Atlantic Gateway site as well
 
Jeff

World Wide Wrestling has a special place in my heart as it was aired at 11:30pm Saturday nights on our local CBS affiliate WTVR, and in my younger years I would painfully sit through the 11:00 news (which seemed to lag on forever) waiting for the show to start.  
 
Hands down one thing that sticks out the most for me was in April or May of 86 between Tully Blanchard and Ron Garvin for the National Heavyweight Title.  This was the follow up to Tully, Arn and JJ injuring Garvin's right hand.  The match and angle lasted the entire show, and it's one of the best I've seen and a sentimental favorite of mine.