Unix got increased presence on Internet because DoD paid UCB to port "DoD Internet" (aka TCP/IP) to Unix, because Digital had announced cancellation of PDP-10 line.
Meanwhile everyone and their pet dog Woofy was exploiting the recent explosion in portability of Unix and thus source-level portability of applications, using unix as the OS for their products - because it enabled easier acquiring of applications for their platform.
With some Unix vendors (among others Sun, which arose from a project to try to build "cheap Xerox Alto"), providing ethernet networking and quickly jumping on BSD sockets stack, you had explosion of TCP/IP on unix but it still took years to get dominant.
Meanwhile everyone and their pet dog Woofy was exploiting the recent explosion in portability of Unix and thus source-level portability of applications, using unix as the OS for their products - because it enabled easier acquiring of applications for their platform.
With some Unix vendors (among others Sun, which arose from a project to try to build "cheap Xerox Alto"), providing ethernet networking and quickly jumping on BSD sockets stack, you had explosion of TCP/IP on unix but it still took years to get dominant.