Cyberpunk is kind of weird as a gaming genre.
The origins of cyberpunk (Gibson, Sterling) were pretty low-key, really. Sure, they had what seemed like crazy ideas and voice compared to other science fiction of the period, but in terms of cyberware, violence, and flying cars, they leaned toward the "realistic" rather than the extreme. Blade Runner predated Neuromancer by 2 years ('82), and I think its visuals were maybe more influential on c-punk gaming than anything literary, but it also didn't feature all that much emphasis on jacked-up black ops mercs using monofilament katanas and smartlinked submachine guns to kill rooms full of sunglass-sporting Yakuza security goons.
RTalsorian's box came out around the time the genre had already started to get adulterated with 80's action movies, MTV, cocaine, and Orientalized depictions of Asia (remember when Japan owned everything?). Cyberpunk was already sort of a self-satire, really; consider the fact that the blackly comedic ultraviolent Robocop also came out in '87. Its a safe bet that more people saw Robocop than Blade Runner (the latter was a big ol' flop at the box office - cult film, yes, but not "popular"), after all. The fact that Cyberpunk 2020 included gangs of people who had bodysculpted themselves to look like Star Trek characters, robotic suits carrying tank weapons, and tons and tons of [strike]superpowers[/strike] cyberware really only helped to accelerate the shift. And Shadowrun; that really opened the floodgates of wackiness.
For me, I think the genre died for realz when Johnny Mnemonic came out. Gibson helped make it, and it wasn't just awful, it sort of singled out everything that was kinda lame and dated about it.
The Matrix has been cited as cyberpunk, but honestly I think its in its own headspace, based not so much on the original material as it is on the pop culture appropriation of it. It did a good job of making Hacking exciting, but aside from that and the greenish cinematography, its not desperate or seedy enough for me to think of it being akin to Neuromancer.