I believe that what happens in this process (which seems to use an ordinary kitchen countertop microwave, such as you’d buy in any appliance store) is that the microwaves produced in the heating process are absorbed by the ceramic kiln, and for the most part do not penetrate to the metal ore itself. (Any that do would simply be reflected back to the crucible and kiln, where they would be absorbed eventually to heat the crucible and flux.) That is, the crucible inside the kiln – and perhaps the flux itself – absorb the microwaves and heat the ore that way. The reason it’s not a good idea to put bare metal inside the microwave is that metal doesn’t absorb the microwaves. However, the microwave oven itself is made of metal, and the mesh inside the glass door (assuming you have a glass door) is also metal.
Although I don’t know what material the flux is, in welding flux is used as an oxygen shield to prevent the molten weld metals (the base metal being welded, and the filler metal added to complete the joint) from absorbing oxygen and weakening the joint while in the molten condition. In this process it seems to be an admixture which obviously won’t react with the gold ore but will hold the molten globules in suspension while they sink to the bottom of the mold (and stay molten for the duration of the process) to agglomerate into the desired shape.
But I’m not a metal smelter; I’m just supposing based on things that I know about welding and some things that I’ve been able to google about metal in microwaves in the past ten minutes.