Why does microwaving napalm make it nonflammable?
In a very similar video I found, some gentlemen microwave gasoline, the flammable component of napalm, along with aluminium foil. The aluminium sparks when exposed to the microwaves, igniting the gasoline vapors in the microwave. Once all the vapor in the microwave is combusted, the microwave must then once again fill with gasoline vapor. When it once again comes into contact with the ignition source, the vapor combusts again.

Since the gentleman in the video you used did not use an ignition source in the microwave, the gasoline in the napalm vaporized, but did not ignite. The vapor filled the microwave, and what was left was the much less flammable gelatin.