Well, thanks for the link!
After looking into this, it appears they have extended their SensorCore SDK so as to include access to the low-power always-on DSP. That is after all just another sensor, so it makes sense. But still, I think that web page is misleading, because the SDK itself can't do anything if the required sensors aren't available on your hardware platform.
If your device has no motion sensor, then the SensorCore SDK can't do step counting. Similarly, if your device has no low-power always-on DSP, it can't handle remote voice activation. At least currently, the SD80x series are the only Qualcomm SoCs that include the necessary hardware.
So, to get back to your original question, this time with more information than I had going in, I'd say it requires both.
For remote voice activation to work, you don't need SensorCore OR SD80x, but you do need SensorCore AND SD80x.