Allah cannot be obeyed directly. He is obeyed through obedience and total submission to His system (Deen). Allah does not come down Himself on this earth. His message and guidance is brought or conveyed to us through His Messengers. After the death of the exalted Messenger whosoever followed him as the trusted leader of Muslims (The caliphs) were obeyed and obedience to them meant obedience to the messenger and Allah. Obedience to Allah needs a living authority and that is why an Islamic state is a necessity. The head of the state is not a ruler or a king. he is a trustee who invokes and applies Quranic values in the land to make it a heaven on earth.
Even when the exalted Messenger was alive, the governors who were stationed in far away places did not turn to him for drecisions. They simply decided matters in accordance with Quranuc principles. Obedience to these 'Ullul Amr' meant obeying the messenger and Allah. The same principle can be applied now but for that you need a pure Quranic government.