What's described is not recovery from a coma. It's recovery from whatever trauma caused the coma. Frankly, you're either in a coma or you're not. You don't need rehab for the coma itself.

Some hospitals also run their own rehab center. It's a different part of the hospital with different functions. Hospitalization ends when you no longer need the medical services. Rehab has likely begun even while in a coma, top keep blood flow, muscle strength, mobility, etc.