It's mainly a terminology thing. Pins 2-9 on PIA II (IC11) are called PA0-PA7 on the chip schematics. They are configurable as input or output, and Leon's test ROM configures them as outputs to give you the pulsing signal to look for. Their function in the context of running a game ROM is to connect to the switch matrix inputs to see when a matrix switch is closed.

I guess the doc's reference to IC10 is a typo? That is the lamps PIA which is not relevant to any of this.

I'm not sure why it suggests doing this twice. As you suggest, it seems redundant.

Have not figured what out?

I think it is not so much of an issue and more just a redundancy. One section is for testing the PIAs and one section is for testing the switch inputs, and it just happens that they overlap.