Yes, you can replace it with whole wheat flour. The recipe actually calls for all purpose flour as it is light and gives a fluffy bread like texture to the puris for which they are called as buns. Recently, I got a query from one of my reader who asked whether she can replace it with whole wheat flour.
I replaced with whole wheat flour and the result is amazing. These buns in the picture are made of whole wheat flour and they are equally good. As whole wheat flour is heavier, it might result in slightly dense texture and slightly lesser fluffiness.