Dragons only die when their soul is absorbed. As in die without possibility of resurrection, because you did not absorb his soul their is a posibility of resurrection and that's why I say he's not dead. It kinda depends on how you view "death" here.
Question then: Why didn't we absorb his soul? Yes, he is the first Son of Akatosh, but all dragons are Akatosh's children. Even if his duty/destiny is greater than all other dragons, why were we not able to absorb his soul? Did Akatosh intervene?