In the beginning, all was silence.
Most of the initial video games (computer-based, home-based, or arcade-based) focused squarely on the visual (I guess that’s why they call them VIDEO games). In fact, until about 1972, video games had no sounds at all. This pretty much set the standard, unfortunately, and music would continue to be more often an afterthought than an essential element even to the present day.
Sound effects were actually more important to many games, especially considering the limitations of early audio components. When your sound source can only play one note at a time (we nerds call that “monophonic”), you’re more likely to dedicate it to the game-enhancing beeps and boops that tell you when you’ve scored a point…or used up your last life.
Pong made a nice little “ping” sound, and that’s about it. However, by the time Space Invaders became a sensation, the developers were already recognizing that the sounds could be integral to the experience. With a tense build-up like a robot version of the “Jaws” theme, the alien heartbeat of the advancing enemies was actually quite effective (the following year, Asteroids took the same basic idea and gave it a tiny bit more depth to go along with the snazzy vector graphics).
Some games tried to get around the monophonic limitation by using creative (and almost exclusively impractical) methods. The Journey arcade game actually came with a built-in cassette player, to fill the arcades with the poorly-reproduced sounds of one of the band’s worst songs ever…over and over and over again. That alone may tell you why you’ve never seen one…or why Steve Perry refuses to sing with the band ever again.
It may not be the first tune whistled on the way out of the arcade, but I’d nominate good ol’ Donkey Kong as the game that made video game music right: it added to the gameplay experience, and was identifiable with the specific game while also being memorable enough in its own right (if only just). I’m sure a lot of people got sick of it, but then again a lot of people got sick of Michael Jackson long before his music stopped (come to think of it, I’m still waiting…).