No. That description is an overly simplistic definition that never made any sense. There were coupes in the pre-War era, and all of them had fixed, solid B-pillars. It wasn't until the introduction of the pillarless hardtop that there was any distinction, so that was around 1950 and lasted to about the mid-1980s. And even then then definition didn't work. In the 1950's the Ford Crown Victoria had a pillar, the regular Victoria was a hardtop. In the 1960's the General Motors midsize A-bodies offered a fixed pillar coupe and a hardtop coupe and in the Chevelle a 2-door sedan. In the 1970s, the GM A-bodies carried the Colonnade styling with coupes with posts. So as a definition, it doesn't work.

In the modern era (from around 1980 on), most car lines stopped offering multiple two-door body styles, and they basically labeled their two-door models as "coupes" and the 4-doors as "sedans" (some sporty cars did continue to offer notchbacks and liftbacks at the same time). So people have come to associate any two-door with the term "coupe". To add to the confusion, manufacturers started making fastback 4-doors and called them "coupes". And now there are SUV Coupes which are neither sedan nor coupe.

I generally go by what the manufacturer calls a two-door body. In the Impreza's case, they called it a "Impreza Coupe" in the US.

http://importarchive.com/brochure/subaruimpreza1995_02