"Does that mean the ELK actually doesn't control the lights. The PC hooks up to both the ELK and the light controller? Meaning, rather than PC->ELK->Lights, We use CQC or something to get signals from ELK and relays that to the HW controller?"
The ELK M1 supports a few lighting systems. Most of of the popular powerline technology ones especially.
There are several PC software automation packages that also can interact with the lighting systems control methods.
many of these external controllable lighting systems use RS232 (serial) or a USB connection (which typicall is also serial communication).
If the software package also supports the ELK panel, you can:
PC <> ELK <> lighting controller hardware <> powerline <> the device
PC <> lighting controller hardware <> powerline <> the device
Or some also support both methods at the same time (you typically need two controllers).
There are pro / cons for each.
The first method doesn't require a PC to be on. Less things in the way, means less things to not work. Keep in mind, that for the powerline systems, you can still control the lights manually at the switch even if the control system isn't running (the good ole fashioned way).
The second method which is PC centric typically will get better touchscreen and automation system response and results (less links in that chain).
The third gets complex to administer and not many "do it". keeping things in synch gets challenging.
So, if automation in your home is "behind the scenes" Do option 1.
If you want to interact with your hardware and do more sophisticated setups, do option 2.
Once you do one or the other, you can play with Option 3 as a hobby