That PSU has only an EPS12v 8-pin plug for the CPU. Try it with just that one plugged in.
The manual says if you only have a P4-style 4-pin connector to plug it into the 8-pin, but then also says to plug in the other 4-pin. I am not aware of any non-server PSU with two 4-pin plugs except those that are supposed to be combined into a single 8-pin, so it's probably fine with nothing plugged in there. It's actually much easier to find PSUs with two 8-pins, or an 8 and a 4.
If you are really concerned about it, it would be best to ask Asrock.
Back in the early days of the P4 connector, there were a lot of sketchy molex-to-4pin adapters around. They were sketchy because they used only one yellow +12v wire.