The author didn't claim drinking alcohol eliminates stress, but rather is a helpful aid when wanting to relax after a stressful day. If one's primary goal is to achieve a state of relaxation, it is possible to do so by taking steps that stress the body in other ways.
Bottom line: the author's statement is not incompatible with distinct definitions/understandings of relaxation vs. stress.
Most people are familiar with the common "I need a drink" reaction to a high stress situation or day. Even most drinkers understand that the alcohol they're consuming is actually stressful on the body in other ways.
Many will gladly trade their current mental/emotional stress for the physical stress alcohol puts on the body, because regardless of eventual harm, it feels good right now.