My understanding is that DE is basically microscopic broken glass. Drying out isn't really the right description. It cuts up their exoskeleton, exposing them to outside "stuff" that the exoskeleton protects them from. So, for an external bug/parasite that might dry them out as one of the effects caused by it. When it gets wet I imagine it could form a crust that those bugs could walk over more safely...This has been my question too. I've been told that the DE will continue to dry out the parasites, but that only makes sense to me when applied externally to soft-bodied worms or if the parasites ingest the product. I do know that naturalists praise things like DE and bentonite for acting like a sponge in the digestive system, sucking up toxins from the intestinal lining so they can be expelled rather than retained to cause inflammation. I know first-hand that bentonite is very effective when consumed by humans and suspect that DE would work much the same way, but much of it is speculation. I know of no studies proving conclusively that it helps in an internal cleanse.
For internal parasites the cuts the DE inflicts could conceivably open them up to the immune system to fight, or to the other bacterias and things in the digestive system that they are usually able to withstand. From what I've read, DE is not a surefire 100% cure for internal parasites. It will reduce the gutload and works well as a preventative, but that's it.