Neither of us have heard of FUDGE. Damage-wise, if I had to pick, I'd say the Friday Night Fire Fight stuff from Cyberpunk 2013 (I think 2013, I remember playing that instead of 2020, though not sure) had the most impact among RPG damage systems, though movies are a much greater influence here. We had some violent little rpgish BASIC games that had bp wounds prior to playing Cyberpunk, I'm pretty sure, though I don't have the file dates to check and it's hard to remember back that far now.
The general desire to get away from numbers and toward adjectives has been there since our early-mid 90s stuff (BASIC dragslay had a few numeric stats and C dragslay had no numbers, which puts it around 93-94, maybe), but I just chalk that up to wanting more immersion and I can't think of a specific influence there in any medium (unless you count wanting it to sound slightly more like written fiction). All the 80s games we used to play were either DND or like it, I think, though I don't remember them all. If a game like Sword of Aragon or Wizard's Crown used adjectives, that'd definitely count for something here. We played a bunch of them. After around ~1992 or so the influence of video games and RPGs drops off dramatically, as we were mostly doing our own thing then and didn't buy as many games and didn't roleplay as much. We played Wrath of Nicodemus (1987), and that had BP damage at least, though we didn't play it until a few years after that came out, so it is probably in the same category as Cyberpunk with the wounds, I think, pushing us in that direction after some initial experiments of our own. I definitely remember the limbs being chopped off and so on, so it was memorable anyway.