What changes does zinc chloride undergo when ‘fusing’ on an atomic level? How does this influence reactivity?
One purpose is to eliminate water as @Waylander has already pointed out. 

Another is to have a clean crystal surface. Aging is a common process of crystals. The surface is transformed slowly. The crystalline structure changes since it is not the same to be surrounded with other atoms (molecules, ions) of the same composition than with nothing or a gas. 

Finally, another purpose is to have a crystal size as small as possible. The smaller the crystals the bigger the surface area, so more is available and the reaction proceeds faster. 
 The small crystals are obtained in the rapid cooling. The faster, the smaller. 

The zinc chloride solidifies in one lump, but there are still crystals. 
They only have grown together. 
If it were a real glass, the reactivity would be the highest since there would be no packing. 
This can only be achieved with extreme rapid cooling. 
When cooling is fast but still takes some time, crystals grow. 
When the cooling is slower, the crystals grow bigger. 
The smaller they are, the more surface the lump has. 

Melting must be done for the other reasons, but when you cool it must be done fast because, if not, you will get a less reactive mass. 
It is not a comparison between molten and non molten product, but between fast or slow cooling of the molten salt.