Only in the sense that all things are ruled by God. If you mean are they ruled by God in the sense of: "Are they Sent by God to do His work?" there are two primary questions that need to be answered first:
1. Who is God? If Allah is 'God' the Creator of all things then the answer to your question is 'Yes'. If the God of the Bible is the Creator of all things the answer is 'No'.
2. Does the Quran represent the teaching of God? Only if Allah is 'God' the Creator of all things. However, if the God of the Bible is the Creator of all things the answer is 'No'.
If the answer to either of these questions is 'No' than we can assume that Allah may in fact be 'the god of this world' (Isaiah 14:12-14 & 2 Corinthians 4:4) , also known as Satan, the Adversary who opposes all things. Look at the actions of Abu Bakr and Islamic State. They oppose all things; they hate the Jews and all followers of the God of the Bible; they hate everything and everyone and everything that disagrees with the teachings of the false prophet Muhammad. If the concept of Religion is to be understood as a specific deity (or deities) being worshiped, served and obeyed by followers, we can see in the actions and statements of Abu Bakr al-Baghdadi and Islamic State a clear indication of where they come from and who they obey.