The deeply robust elder Deaf community itself is proof that the brain tissue loss described in the article is probably not due to the hearing loss itself. I have never heard of a culturally Deaf individual experiencing this kind of degeneration of the brain. If I had to hazard a hypothesis it would be on the social end of things, such as social isolation causing decreased function, similar to to the social contexts that encourage addiction.
In other words, when one loses hearing, the culture around them fails to accommodate that leading to increased anxiety, stress, and other kinds of undesirable outcomes that are shown to impact health. It is immeasurably tragic in many ways that this phenomenon is being used to sell hearing aids and more anxiety.