Immediately after Austin delivered the 3:16 promo, people connected with Stone Cold and became fans.
"Austin 3:16 says I just whupped your ass!" is what launched him. Yes, it needed follow-through, but that's where people took notice. I think he could have created another moment down the road and he was obviously talented enough to make it, but it's really tough to say whether Stone Cold Steve Austin would have been "Angry Stone Cold Steve Austin" without the KOTR push.
Other comparable promos to Austin's would be the Rock joining the Nation, CM Punk's "Punk Pipebomb", and Scott Hall invading WCW.