Defeating a great power is the accepted test of a great power. That is how great powers have been recognized by scholars, statesmen and military observers through the entire history of the European balance of power.
Being the regional hegemon of the Persian Gulf, and let's just accept that premise for the sake of the argument, doesn't make you a Great Power, no more than the Houthis are a Great Power because they can shut down the Bab-el-Mandeb for a while. And this is hardly a game changer anyway, as Iran already had de facto control over Hormuz.