Is Microwaving considered dry heat or moist heat and why?
It is not inherently either, but most often it performs similarly to moist heat.

Microwaves work by directly exciting polar molecules within the food, usually water or fats.

If the food contains significant quantities of water (like most fruits, vegetables, meats and so on) then microwaving usually acts very much akin to steaming, which is a moist heat method.

In some fringe cases, most particularly bacon, where there is a significant amount of fat that can be directly excited to temperatures higher than water can obtain without evaporating, you can essentially fry by microwave... and of course, frying is a dry heat method.