I'm probably not the best person to explain why decision theory is interesting from an FAI perspective. For that you'd want to ask Eliezer or other SIAI folks. But I think the short answer there is that without a well-defined decision theory for an AI, we can't hope to prove that it has any Friendliness properties.

My own interest in decision theory is mainly philosophical. Originally, I wanted to understand how probabilities should work when there are multiple copies of oneself, either due to mind copying technology, or because all possible universes exist. That led me to ask, "what are probabilities, anyway?" The philosophy of probability is its own subfield in philosophy, but I came to the conclusion that probabilities only have meaning within a decision theory, so the real question I should be asking is what kind of decision theory one should use when there are multiple copies of oneself.