Maze, later expanded and renamed to Maze War, is a 3D networked first-person shooter originally developed by Steve Colley, Greg Thompson, and Howard Palmer for the Imlac PDS-1 computer. It was largely developed between the summer of 1972 and fall of 1973, at which point it included shooter elements and soon after was playable over ARPANET between multiple universities. It is considered the earliest first-person shooter; ambiguity over its development timeline has led it to be considered, along with Spasim (March 1974, on PLATO), to be one of the "joint ancestors" of the genre.
Very few people would have been directly influenced by Maze War. Most people would have got their first exposure to such games by playing either Escape! or Ratrun. The Digital Anitquarian has a nice write-up on Escape! He reveals that Lord British was inspired to write Akalabeth by Escape! .
These early attempts at rendering a virtual reality are hilarious when compared to today's ray-traced wonders, but every software revolution has to start somewhere. And Ratrun is part of that revolution-- a very BASIC part. Because it was first published in Cursor Magazine (#13) it would have got fairly wide distribution. People could simply borrow the magazine from a library and type it in for themselves. Very few would have been able to purchase Maze War, but very many might have had their first experience of a computer generated artificial reality in the form of the slowly rendered lines of Ratrun running on a school PET. As one commenter on the video of my version states "Such fun to see these old machines work like the ant that could." For more info see:
And here's a WAV file for those who would like to try it on real MC-10 hardware: