This feels too reductive to me. In particular, it makes a hard distinction between the thinking and the language. I fully accept that they are distinct, but how distinct? It is hard not to think that some thinking styles influence how something is heard?
Not just in full language, mind, but consider the last time you heard a song in a major key? Do you even know what that means? Because many of us do not.
Same goes for listening to people discuss things like sports. I'm inclined to think many people effectively run a simulation in their mind of a game as they listen to it broadcast. This almost certainly isn't inherent to the language, it is part of the learning of it, though. Think looking over lists of the moves in a chess game. Then go from that to laying out the pieces as they are after that list. Or calling what the next move can be.
Can this be a completely separate set of "circuitry" in our brains that first parses the language and then builds the simulation? I suppose. Seems more likely there is something that is active between the two that can effectively get merged in advanced practitioners.