(I get that in Paul Graham's original intent for HN there's no religion, and the following is also very intense, but now that we're talking about religion and death I feel right about this.)
Well what constitutes war against GOD, referred to as "Allah" here, and Mohammed (my choice of words reflect that I consider him a real prophet, but specific to Islam, not Christianity, it's subjective like fame) is not elaborated on, probably in another section it goes into detail, and plus you have to use this old, outdated tech that isn't compatible with anything these days, "judgment." Nobody talks about it much anymore.
As for the specific punishments for that harm, it's not vague at all. Execution, OK so in Arabia that means you put their neck on a chopping block, made of wood for the same reason as a kitchen cutting board, a man with a mask whose job title is "executioner" walks up with an axe I think it is, I don't know I haven't watched them live but I know in Saudi Arabia it happens in the public square, some same place every time, everyone can go watch; the masked man lifts his axe, well from that point it's too graphic even textually for HN. Then crucifixion, it's the destiny of Christ, for good reason because that was the most feared form of torture and death in the Roman Empire. Then finally, the other punishments are lighter, and the opposite-sides rule for severing hands and feet is a way to be merciful so the punished blasphemer can walk on crutches at very least, not be absolutely crippled. Exile sounds light but it's rough, most people end up at the bottom of society if they're exiled, second class citizens and often slaves. Obviously much better though. So that's where judgment comes in, this isn't digital, it's much more consuetudinary. The judge can decide what the punishment will be commensurately with the unique nuance of the transgression.
I hope that clarifies the vagueness.