And, one could, from the context and later clarifications, take Gailey's comment to mean exactly that: when CJ gets winded, he takes himself out of the game. And, like you mention, CJ confirmed himself that he did in fact take himself out of the game.
BTW, didn't Thurman tweet something about how he'd never have taken himself out of the game to catch his breath or whatever one wants to call it? He might have told Jim to call someone else's number in the huddle, but he'd never take himself out.