After Mr.Dimmesdale confesses, why does it seem that life has departed from the face of Chillingworth??

This is because he no longer has control over Dimmesdale.

Chillingworth has made his life "worth living" because he wants to punish the minister and the sins about which Dimmesdale feels guilty. Once Dimmesdale has confessed, Chillingworth has nothing else to live for or to motivate him to live.