Sound Blasters and compatible cards used IRQ lines because back in the bad old days CPUs were slow, bandwidth was tiny, and buffers were minuscule.
To get responsive/real time audio the card needs to signal to the CPU, not the other way around, and at the time IRQs were the way to do that on ISA busses.
I would imagine that ISA cards that didn't need IRQs either required CPU polling or DMA.
I imagined that the game / audio driver would just send data to the card at regular intervals and that's it. I realize now that the card uses it's own clock that can drift when compared to the system timer and this method would have a buffer underrun/overrun problem.
To get responsive/real time audio the card needs to signal to the CPU, not the other way around, and at the time IRQs were the way to do that on ISA busses.
I would imagine that ISA cards that didn't need IRQs either required CPU polling or DMA.