I got an answer at another forum that this 6pin PSU-6pin PCIe cable is not for my PSU, it's from another model of Chieftec - that's why it doesn't work.
I was suggested if I connect 6pin PSU -> SATA cables with SATA -> 6pin PCIe then probably it will work.
Some people are doing so, it seems like it's working fro them, other ones are telling that it can burn connectors or even the device.
I'm still not sure if I should try it.
Yikes - that makes it a tough call. No other way round it? I couldn't plug something in that could potentially burn connectors or worse. All I can say is there have been lots of rig fires. Err on the side of caution.