The description of The Stuff of Nightmares implies an immunity to fatigue causing critical effects, unless done by psychic/holy means, does this extend to regular fatigue? Why or why not?

Per the wording, it's not so much an immunity to fatigue, as it is the critical effect that would normally cause fatigue is ignored.

Fatigue from a non-critical effect would not be affected by Stuff of Nightmares. That said, anything with Stuff of Nightmares probably also has a high Toughness Bonus.

Here's an analogy: paintballs don't break open when they hit you (because magic) - you're immune to getting covered in paint by paintballs, but if somebody dumps a can of paint on you, you're still covered in paint.