So there are a few things that make a transfer case and most 4WD systems generally better for off-road. The biggest two are gearing and how durable/robust the systems are.

The ability to change the final drive gives incredibly low gearing to 4WD vehicles. This provides increased torque for traversing obstacles and better low speed control.

In the durability front, that is largely due to design considerations. AWD vehicles are typically designed for on road use, so the engineers built them with that in mind. This means lighter and weaker drive shafts, weaker steering racks, less robust suspension, and generally lighter duty pieces throughout the entire system. 4WD vehicles usually designed with heavier duty used in mind (even if the majority of people won’t use them that way). This means the entire drive train is built stronger and more capable of abuse.

This is a huge generalization though. You could build a purpose built AWD off road vehicle with low gearing, and locking differentials if you wanted. And there are plenty of 4WD vehicles that wouldn’t survive even moderately difficult trails. So the NPS probably made the rule because generally 4WD is more capable for that use case, and it would be difficult to make an all exhaustive list of what vehicles or components would give you the capability to navigate the trail.