FIRST OF ALL, i don't really care what kind of points bytebeat gives. now that that's out of the way:
the only fundamental thing about a sound chip is that it converts digital information to a specific type of analog signal. different chips have vastly different capabilities; the distinction of "modern" sound cards is that they can convert any, say, 48 kHz 24-bit PCM (read: any digital audio recording) that you throw at it to an analog signal, and as much of that as your computer has memory for. the possibilities are infinite.
the important thing, from my perspective, is that the digital information that you give modern sound cards—as opposed to the chips that we normally associate with "chipmusic"— is already a direct representation of an analog waveform, accurate to within its given bit depth (and sample rate, if below the nyquist rate for human hearing). under (unrealistically) ideal conditions, if you played a WAV file (using a digital-audio converter, or DAC) and recorded the output into another WAV file (using an analog-digital converter, or ADC) , you would end up with exactly the same information you started with.
by contrast, for the chips associated with chipmusic, the digital information given to the chip is usually a series of writes to its various registers at various times. sometimes a degree of PCM is also supported, but then hardware mixing is used (see: the paula chip from the amiga computer). the point is, some type of software interfaces with the sound chip, but the sound chip does the work of generating the resulting audio signal.
does that make sense? i might have rambled a bit.
so if we were determining format class by the metric i just implied, then i think bytebeat is pretty solidly in the mixist camp since you can generate arbitrary junk; it's just harder than if you were using a DAW or some other software. BUT like i and others have said, the format classes are not determined this way so who cares whatever.
maybe irrlicht could offer a different perspective since he's written various 1-bit music drivers, which are sort of their own type of animal.