"When I said party I meant parry. Here's a famous video showing the parry system at work, as you can see it has nothing to do with wrestling games."

That was an awesome vid. The parry system did change the fighting game dynamic a lot. Wrestling games, including WCW vs World, had counter moves for various strikes and grapples. I don't recall them making opponent go backward to deliver arbitrary, normal move. So, SF3's parry's are either original or an enhancement on wrestling counters. Definitely innovative for that kind of audience.

"Also, regarding 8-way run coming from wrestling games, they aren't the same mechanic. In early wrestling games you need to press a run button to run, and when you do your potential moveset changes. Furthermore, your run is not relative to the other player but rather relative to the ring. This all gives it a completely different feel."

That is true. It's why I added Ehrgeiz whose movement makes Soulcalibur look really limited. Maybe I'm misremembering it, though. Look at link below. Scroll past character descriptions to section IV: "basic moves and fighting techniques."

http://www.gamefaqs.com/ps/197216-ehrgeiz/faqs/4749

You'll see it had full, 8-way, arbitrary movement with 360 degree attack angles possible. Also crouching behind stuff in level, jumping on level, weapons, rolling, ground attacks, counters, tech hits, and instant 180's. It lacked the smooth flow and ease of use of Soulcalibur as players had to, a la Tekken, face the opponent's attack and direction precisely to counter it. So, you felt mastery when gameplay looked like a Soul game.

"Lastly, Soul Calibur is not in the same lineage as Tekken. As I've already said, Soul Calibur was the sequel to Soul Edge. It's a completely different game series."

The old making of soulcalibur writeup said the Tekken 2 team helped make it. It's why I thought it was a sequel to Tekken at first. The SC and TK2 team worked together on it. Presumably reused techniques in codebase from TK2 since they clearly weren't doing the artwork. That's speculation but SC was a team effort that included TK2 team. It's a joint lineage even if separate mechanics and artwork. Don't know why it bothers you as it's more like a good FOSS partly forks or works with another good FOSS to create a perfect-rated FOSS. I plan to replay it in future just cuz you had me look it up.

"Before I answer that question, please answer this, do you know of any games that were game-changing or way ahead of their time on PlayStation 1?"

Metal Gear Solid. Whole volumes written about playing in a movie, enemies' reactions to things, clever ploys by designers, stealth aspect... whole package. Landmark work that only a few tried (and failed) to copy.

WCWvsWorld or WCWvsNWO. Came out same year with similar mechanics including 8-way movement (ring-based as you said), grappling system, counter moves, team matches, weapons from crowd, and so on. NWO probably the innovator here. No Mercy and others copied it. WWF Smackdown would later take 3D wrestling back to fast-moving, high-flying, crazy roots in arcade games. Then, PSX vs N64 debates re their various games were more accurately New PSX vs Old PSX styles but N64 people pled ignorance of WCWvNWO or WCWvW. ;)

Twisted Metal. There's racing games. There's destruction games. There's 3D world games. This combined all three into what I guess was a new genre as people acted like they never saw it before.

Final Fantasy VII. I never played others before it on console so can't say anything to mechanics. Yet, combo of deep story, character development, and custom, classical score matched to events in game made a powerful impression I had never encountered in another game. That combo seems unique, esp leveraging classical for emotional impact. So, it's a maybe but I'm not certain.

Resident Evil. Characters, interesting plot, puzzles, unusual game mechanics, and scary kills pioneered survival horror genre in consoles.

Sports. I recall Playstation had some of first, sports games like NBA that mimicked life-like stuff instead of arcade stuff. I'm not sure if it was first on this but it was first I saw that reminded me of real-life.

Alright. There's a start. Feel free to accept or shoot them down with counterexamples.