These predictions were very commonplace by then. In 1983, TCP/IP came along and MILNET was split off. This is commonly considered to mark the start of the Internet. First .com domain was registered in 1985.
The further twist is that just a few months after this interview, Jobs left Apple and founded a company to build graphical, Ethernet-connected, UNIX-based personal workstations: in other words to compete on Sun's turf. I think the Sun/Apple and Sun/NeXT relationship is an interesting, underexplored part of an overtold story, especially since by 2000 Apple had more or less stolen Sun's original clothes as a profitable vendor of Unix workstations.