Can agar be melted in oil?
Here is the molecular chemical structure of agar.
https://en.wikipedia.org/wiki/Agar#Composition

It is a polysaccharide and like all polysaccharides will be strongly hydrophilic.  To answer the question: there is no way a molecule like this will dissolve in oil.  You might be able to make an emulsion but you would need an emulsifier and there is none I recognize in this recipe.
As regards the larger question of why this recipe calls for agar I do not know.