The idea was to follow up Ms Pac-Man/Galaga with another great classic game combination. Centipede is a natural, of course, since it's almost as revered as Ms Pac-Man. Millipede seemed an obvious companion, since it's a more intense version of Centipede. Missile Command appeared to round out the trio nicely, since it generally appeals to a different audience than Centipede in the same way that most people tend to really like Ms Pac-Man or Galaga but usually not both.
The first problem is that Missile Command used a horizontally oriented monitor while Centipede and Millipede's monitors were turned vertically. This meant that we'd have to rotate the image on Missile Command and lose a little image off both edges (8 pixels each, as it turns out). Fortunately the player's crosshairs couldn't move into that space anyway, so it didn't greatly impact the play experience (purists of course will disagree).
The hardware for Missile Command is very different from Centipede and Millipede so the techniques of the Ms Pac-Man/Galaga game couldn't apply. Instead, we used a programmable chip that we could reconfigure very quickly while the game is running. So, during that 1/8th of a second or so when the screen goes black while it switches games, it's actually reloading the hardware with a whole new design to run the next game.
The game wasn't earning quite as well as the Ms Pac-Man/Galaga game, so to push up the earnings a fourth game was added: Let's Go Bowling! It's a simple, top-down bowling game which we wrote in 2002 using only hardware that was available in 1980.