Brutalist architecture was largely driven by enabling concrete technology. Concrete was previously used as a purely structural element, but as it advanced, architects realized it could be used as an aesthetic. IMHO, I believe that when these architects built these buildings, they were aiming for something more human, like shaped clay, but their efforts simply failed, and they created something entirely different. In fact, there was never any coherent brutalist architecture "movement", most brutalist buildings were deemed so long after they were built, largely because they appeared foreboding, intense, and used large quantities of concrete. (yes, there are plenty of "brutalist" buildings that don't heavily rely on concrete, but there's no question that many of the most famous buildings do so).

So I don't think brutalist architectural design necessarily means exposing the "base structure". I would not consider the pompidou center as brutalist.

Brutalist web design is also foreboding and intense, but that is really the end of their similarities. Many brutalist web designs intentionally create a disjointed feeling, overlapping text, mismatched fonts, large variations in color and font-size, are intentionally used to create a particular feeling of haphazardness and authenticity. I don't think brutalist architectural design carried that same intent.