Actually, Quake may be the first American game with a soundtrack made by a recording artist, but there are at least two British games predating it in which professional musicians were involved.
The first computer game I remember having a soundtrack specifically done for it by "mainstream" artists is the Amiga version of Xenon 2: Megablast, a Bitmap Brothers vertical scrolling shoot'em-up from 1989, whose musical theme was composed by Bomb The Bass.
Also, in 1995, Ocean's 3D shooter Inferno had original music by Alien Sex Fiend.