Are there other types of ways of dying from airway obstruction?

Yes and more so: Depends on which kind of obstruction you mean. There is intrinsic, inside the airway(larynx, trachea, bronchus) and extrinsic which is compression of these organs such as by a large blood clot or cancer or strangulation. And then there COPD which is obstruction at the lower part of the airway where the alveoli and bronchioles are. It would help if you were more specific.