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.
This is short sighted. Trading temporary relaxation now for worse stress down the line. Alcohol consumption increases stress over the long run.
It’s just as important to examine and understand the psychological drivers behind drinking as it is to understand the physiological impact.