It doesn't say exactly if the "drunkenness" issue is to keep him out of Ol' Sparky, or what. They might use it to reduce murder one to murder two. It can reduce murder one to murder two if it negates the defendant's deliberation, premeditation, or intent.
Manslaughter is usually divided into two kinds, voluntary and involuntary. Voluntary = intentional killing in the heat of passion after the killer has been provoked. Involuntary = gross negligence plus a death or misdemeanor + a death.