Interesting! I was exposed to a "3D" dungeon crawler (Wizardry[0]) on the Apple II in September of the same year.
I do wonder if 3D Monster Maze truly qualifies as "the world's first ever 3D game on a home computer" given that the lead programmer didn't own one of the machines until April of '81 and that the commercial release occurred the following year (at least according to the article on Wikipedia - the sidebar says published 1981 so it's contradictory).
The birthday anecdote seems plausible but if Wizardry was in development for more than six months then it predates 3D Monster Maze.