The write-up and TFA conflate the Internet and (what became known as web). Maybe, the slines don't know any better, but Slashdot users ought to... The hyperlinked documents weren't the first "killer application" — e-mail was. The first systems weren't even using the Internet, but, according to Wikipedia:
And Sir Lee's was not even the first system for linking documents/files across the networks — Gopher was. And Gopher was not merely proposed in 1991, that's when an actual system became available (though protocol was codified in an RFC only in 1993).
If you want to get "technical" the web (aka http/html) was first (1990 vs 1991 for gopher), but the graphical browser mosaic didn't appear until '93 and not to many folks were using the non-graphical web servers that were in existence at the time.
If email was the killer app, inter-domain mail (via unix mail via rmail/UUCP) was probably the real killer app, not ARPANET email as ARPANET was mostly restricted to non-commercial use. Gopher like the "web" didn't really pop up until '91 when the NSFNET (the modern "internet") was winding down and the commercial internet was ramping up (the various NAPs like MAE and CIX, etc were taking off). Prior to inter-domain unix mail, commercial email was generally *unconnected* (needed to be on the same proprietary system like compuserve to send/receive mail).