What is a non-Darwinian theory of evolution one might ask? All theories for which the main mechanisms of evolution are not chance and natural selection. All this surely does not mean to say that in these theories, chance and natural selection do not exist. But they are not the main factors driving evolution. They only play a secondary role.
There are certainly speculations based on postulating that « the main mechanisms of evolution are not chance and natural selection » but certainly not scientific theories I’ve heard about.