After many hours of examining this (and no thanks to you Asus support, still waiting your reply), I am pretty sure that Asus Z170-A motherboard cannot be powered up by USB keyboard - only by PS/2 keyboard. Note - UEFI is latest version, Legacy USB is enabled.
Here is what I tried - setting Battery Charging Support to Enabled - when set to Disabled - the USB ports are essentially dead when system is powered off - that is S5 state (S5=soft off - more info on https://msdn.microsoft.com/en-us/library/windows/desktop/aa373229(v=vs.85).aspx). Made sure that the USB is really powered by plugging in mouse - the LED was lit indicating the USB port was powered. Still, it did not react to keyboard (any of the options, as offered by Advanced Power Management (APM)).

Furthermore the Advanced Power Management (APM) specifically calls this option Power on by PS/2 keyboard - in fact, if the PS/2 keyboard is disconnected and only USB keyboard is connected, this option completely disappears.

My conclusion is that the system can only be powered on by PS/2 keyboard type, not by USB keyboard, on this motherboard. Some motherboards might have power-on by USB keyboard but I think not this one.
Still, it is not all lost - possible solutions I might use (and others might be interested in as it might be of use for another motherboard as well):
Using a "Combo" (USB and PS/2) keyboard. USB to PS/2 adapter does not work on all keyboards as it does not translate signals. It only works on keyboards which already have circuit to automatically switch between two modes, by auto-detecting which connector is plugged in. These keyboards have so called "Combo" interface. They are harder to find than USB-only keyboards these days though. I'd guess 90% of keyboards use USB-only interface nowadays.
Attaching a programmable keyboard (such as X-keys XK-24) assuming this kind of keyboard can be attached to PS/2 port (for example has a "Combo" interface) and can be programmed to send "Power On" code. I guess X-keys is the best bet as it is pretty much customizable but not really on the cheap side. I also found Cherry G84-4700 but not sure if it can be programmed this way either. Generally - programmable keyboards can store macro / key commands in their internal memory, they don't require software to operate, once programmed and thus, this might be a way to power up a system assuming a correct key-scancode can be assigned to a key.
Attaching an older PS/2 keyboard just for the powering up purposes and use USB keyboard when powered up (kind of dumb to keep entire keyboard on desk just for one key, but hey, it is a solution). Or using some smaller form PS/2 keyboard, same thing.