The difference between drunk walking and drunk driving is that, while a drunk walker is a danger only to himself, a drunk driver is a threat to others.
A drunk walker careening into traffic poses no threat? Must note the "level" of drunkenness; motor skills at acceptable level but "above" limit per-law? You can still get public intoxication fines / jail, as well as a DUI if you hop on a bike (also highly dangerous).