I agree with Marc. What made the web win was that random people could make web sites. So there started to be way more stuff on the web than on AOL. By late 1995, the main reason people were signing up for AOL was to get access to the web.
He's talking about an earlier and much more ambitious AOL than you are. AOL once hoped to be what later turned out to be the web. But because they weren't open enough, the web grew faster, and they became merely an on-ramp for it.
(Then after a few years of being a quite prosperous on-ramp, they lost even that, which is the vanquishing you're thinking of.)
