I'll assume the home has a solid foundation and is not open. If that is the case I hope it is not damp because then no home would be allowed to have nm run under it. IMO, it is not considered damp.
The last time I had an inspector try to say that a crawl space was a wet or damp location, I simply asked, do you think the builder need to use all weather proof construction for all the lumber exposed to the crawl space like treated wood? he left me alone since he knew he would not win that battle, if a crawl space is that damp there is going to be more problems with this structure then the electrical wiring.