ARPANET and its successor TCP/IP already provided the fundamental networking infrastructure. Various hypertext systems were also being developed independently in and before the 1980s, like Ted Nelson's Xanadu project and Bill Atkinson's HyperCard. The key ideas of linked documents and markup languages were "in the air" so to speak. However, CERN provided some unique conditions that helped the WWW succeed where other systems didn't. It had an immediate practical need - helping physicists share information across institutions. It was developed in an open, non-commercial environment that encouraged sharing. CERN made the WWW technology freely available without royalties. The international nature of CERN helped drive early adoption across countries.

Without CERN, I think we would have eventually seen some form of hyperlinked document system emerge from either academia or industry, but it might have been more proprietary or fragmented.