This definition of heat is given by Max Born. Simply put, heat is any kind of energy transfer to/from a system other than work.

Yes, strictly speaking, microwave heating and resistor heating are examples of dissipation work. They are not heat. However, from macroscopic point of view, many kinds of dissipation work can be safely treated as heat without any problem. That's why we usually call the two examples above "heating". If you think hard enough, even the simple heat conduction by contact is also a kind of dissipation work, which is done by higher-speed molecules to lower-speed molecules during collision. That's why I said dissipation work is a gray area in the definition of heat.