I think it's the same as the parallax floors in Street Fighter II (on the Mega Drive). Unlike the roads in Lotus, there are no hills in the Mega Drive and Amiga versions of Street Racer, so the image only needs to be moved horizontally a scanline at a time, but never moved up or down or stretched out. The only difference is the road texture is animated, which I guess is done with a looping, pre-rendered animation.
I'd love to see this technique extended to handle hills and switching textures. Imagine if each road texture animation has for example ten frames, then you could load in three or four different road textures and swap between them, scanline-by-scanline downwards when the track came to it, so it'd just look like you're approaching a new road surface but it would still be able to dip and turn with the previous one.
Also, Amiga is superior to Mega Drive when it comes to Strip Poker games.