This being cyberspace, I'll assume you've read the Wikipedia article on cyberpunk by this point (if not, you probably should; it discusses how Bladerunner and, to a lesser extent, the Dick story that inspired it fit into cyberpunk). I'd say a better explanation of the blended term is that cyber is the technology and punk is the sociology, but that's still an approximation. Cyberpunk usually means computers at the very least, but since cybernetics technically doesn't require computers cyberpunk doesn't either (it's just very difficult to do without them). Johnny Mnemonic (also at the previous link, and far better than the film) is classic cyberpunk, for many reasons, and I'm not sure any computers are ever SEEN, just RAM in the protagonists skull and the prosthetics in Mollys face, fingers and nervous system (though cybernetics would be necessary to make those work, just not computers).

Wikipedia lists no less than ten cyberpunk derivatives, so almost any *punk is nominally viable some (steampunk) more than others (splatterpunk). Anywhere processing information, particularly proprietary/restricted information, is a major part of the society is open to cyberpunk, really. Perhaps that's part of why it borrows so much of the noir in spy novels like Ian Flemings and Tom Clancys, and Depression era detective stories that feature no technology more complex or advanced than a snub nosed .38. Rome would be well suited to it; you could even have magepunk (though in my expreience that combination tends toward the awful). The example I used in one of my responses to Dan of a Fifth Century Druid integrated with a Stonehenge computer might be considered stonepunk, or at least bronzepunk. It might work better as stonepunk, with the Druid an outsider rebelling against a Neolithic establishment by "finding his own use for" their new monolithic calendar, and bringing about the Bronze Age in the process. Bladerunner provides a date (2019; I can't recall if that was in the short story) but after reading the Sprawl Trilogy three times, and even though I was actively looking for a date this time, I have yet to find one.