When I read this I thought you'd discovered that the whales release the gas in a form other than by blowing bubbles, or that the purpose of doing so was for something other than improved sleep.
But no, the whales literally release air through their blowhole in the form of bubbles, and, at least during study you linked, they do this while resting to maintain their vertical orientation. An orientation, the paper theorises, that enables better sleep by not being buffeted by waves.
They quite literally blow bubbles to achieve restful, vertical sleep.