IIRC 8088 mph has to go to great lengths for the timings to line up, using cycle counting instead of interrupts for timing, among other hacks/shortcuts. I'm guessing that typical 386/486 CPUs were powerful enough to not need this level of optimization.
I agree, even as a young kid with no idea how make the speaker even go beep (I was young, ok?) hearing the music/speech coming from Mean Streets was amazing. Everything else up to that point was just beeping and blipping... IIRC the volume was very low though.
And having now read the article I see it mentions RealSound, albeit not Mean Streets. The digitized speech was something else when I heard it. Game too, for that matter.