There are a few more steps to it. In the renaissance "Gothic" became synonymous with "medieval" because the tribe of the Goths was considered as having destroyed the Roman empire. Hence the name "Gothic architecture" for a medieval architectural style (even though it has nothing to do with the Gothic people). During the romantic movement, the medieval period became fashionable as a setting for romantic and supernatural stories, the "Gothic literature". Horror classics like Frankenstein and Dracula grew out of this genre. This in turn inspired the Hammer Horror movies, which in turn inspired the post-punk music esthetic.

So the subculture is not directly inspired by the architecture, but the architecture and the horror genre is the two places where the term Gothic still used, while the previous meaning of "medieval" have gone out of use in English.