The defining moment for the Royal Rumble was Ric Flair's win in 1992 - until then the Rumble itself was just a diversion, the stakes weren't that high and although the matches were entertaining they weren't considered to be "big time". Survivor Series, an older more established PPV was seen as a bigger show at the time. Flair's victory was significant for a couple reasons...
First, prior rumbles had been won (mostly by Hogan) by larger guys who came in late. Flair's win proved that the right performer could captivate the crowd with a longer performance, setting the stage for the dramatic rumble performances of Rey Misterio, HHH, and Shawn Michaels in later years
Second, this was the first rumble that meant anything significant to WWE stories as the World Title went to the winner. Since then the rumble winners have been granted titlem shots at WM making the match itself important. Prior to Flair in 1992 that was not the case, making this the truly first rumble match you had to watch to see who won.
Flair's coming to WWE was huge at the time, something that wrestling fans never thought would happen in a million years at a time that top stars did not move freely (or often) between companies. Flair's victory in the rumble nearly put WCW out of business, causing major shakeups in their approach to signing talent and running the company. It's fair to say that Flair's defection to WWE and subsequent title win may have set the stage for the WCW that was to come in a few years as the old guard mgt was repalced and Eric Bischoff moved up in the company, setting up the wrestling rivival circa 1996-1999.
Since 1992, the rumble has been almost required viewing and has set the stage each year for the next 4-5 months of feuds/matches, leading into WM, the biggets show of the year. That might never have happened if not for 1992