I’d said what I thought of the word in the other thread, but I figure it’s only fair to answer my own question over here.
If someone asked me if something was available on video, my first thought would be that they meant DVD, as that’s the default video format for most movie rentals at the moment. The addition of “on video” would be assumed to simply be one of those gratuitous qualifiers that people make for clarification (perhaps they think if they don’t add it, I’ll assume they want to ask if I, personally, own the movie). If I offered them a DVD and they said, “No, on video,” I’d then at that point realize they meant they wanted a VHS.
Outside of the context of the movie rental, though, I’d just assume they were referring to a visual recording and there’d be no particular medium that I’d automatically associated with it. The context would be my clue.