By the time Hennig held the AWA World Heavyweight title, it was indeed a shell of its former self. However, as someone very familiar with pro wrestling at that time period, I can assure you the AWA title was still considered a major World title if for no other reason than its rich and storied history.
In fact, when Jerry Lawler defeated Hennig for the title, the pro wrestling media made a huge deal of it. After all his many, many years of ruling Memphis, and going to time-limit draws and disqualification victories over guys like NWA World Champ Harley Race, "The King" finally won a legit World Title.
Even though the AWA title was in a state of serious decline when Hennig won it, he and then Lawler, who defended the belt against Kerry Von Erich throughout his Memphis territory and the WCCW (later USWA) in Texas, some new life was breathed into it.
By the time the AWA finally put the strap on Larry Zybysko, who won it for the first time with an extraordinarily weak battle royal victory over Tom Zenk, that was all gone. "The Living Legend's" reigns only lasted as long as they did because AWA barely put on any shows by that time.
Had Verne Gagne only allowed the organization to grow with the times and rewarded wrestlers who were extremely over with the fans if not the most technically sound (like Hogan and, later, Scott Hall) AWA might have actually survived. Once again, another federation fell to bad booking and looking to the past instead of the future.
It should be noted that one of the easiest ways to determine whether or not a title is actually recognized as a "World Title" or not is use Pro Wrestling Illustrated and its sister publications as a gauge. They have been very selective in assigning true "World Championship" status to various organizations' titles.
For example, the original ECW title was never considered a World Title. However, NWA/WCW, WWF and AWA were. Later they assigned the ECW title "World Title" status. Now they also recognize TNA as a "World Title," I believe.
Organizations like World Wrestling Council in Puerto Rico, World Class Championship Wrestling (WCCW in Dallas) and United States Wrestling Association (USWA, in Memphis) were all major regional promotions which never achieved World Title status.