I have a class this semester where the professor started the introduction to linux with a story about UNIX, saying it originally was conceived so two AT&T/Bell Labs employees could play Pac-man over a network. I can't find a reference to this story anywhere.
It wasn't Pac-man, it was an earlier simulation video game called Space Travel. https://en.wikipedia.org/wiki/Space_Travel_(video_game)
That game was first played in a costly mainframe (GE 365 computer). They needed to run the game in a cheaper and more efficient machine. Space Travel's author, Ken Thompson, found an earlier computer (PDP-7) he could use, he wrote a very basic operating system and development tools, and then ported the game to the PDP-7.
Bell Labs team then later ported that OS to a newer computer (PDP-11), improved the development tools (adding advanced text processing) and it was used in house in Bell Labs. Then later, it was licensed to other companies and educational institutions (they used in OS courses). There are some UNIX variants today, some from companies which licensed UNIX (HP-UX, Solaris, AIX, Mac OS X,etc), some derived from academy (the BSDs aka Berkeley Software Distribution) and some open sources clones (notably Linux).
Linux creator, Linus Torvalds, built also a Pac-man clone, but its unrelated to his work in Linux, and unrelated to the development of the original UNIX.
That doesn't seem possible since Pac-man didn't exist until 1980 and UNIX was made in the 70s with roots in the 60s even. It's possible some modification or variant of UNIX was made for that purpose (there were many around that time such as HP-UX, Solaris, AT&T Unix, etc) but I do wonder what exactly they were trying to network as Pac-Man is a single-player game.