"I have a feeling anything I can come up with you will call an expansion (or something along those lines) to an older game you liked. It's a cop out. For example, Tekken wasn't the first 3D fighter, Virtua Fighter came first, so you could say Tekken was a variation on Virtua Fighter rather than looking at it on its own merits."

Memory loss kicked in here: forgot Virtua Fighter's details since I didn't play it. Further research showed it wasn't just the first (knew that). It had all the key innovations in it that others, including Tekken, copied. So, Virtua Fighter is the game-changer or prime innovator here with Tekken's improvements how it went very mainstream. Soulcaliber improved on Tekken 2 to make it the first one with totally smooth experience. Correction accepted. :)

EDIT: Another in this lineage, same company and year as Soulcalibur, was Ergheiz. It came out before or right with Soulcalibur on PSX limited hardware. It was a bit weird but quite unique. It had Final Fantasy characters on top of others, weapons, 3D environments, moving levels, use of environment as weapon MAYBE (memory...), upper floors, and movement all over. Also, RPG built into it from Square. Movement and blocking sucked. Really weird. 1st fight shows style & range of movement with 3rd showing multiplatform. Talk about ultra-3D.

https://www.youtube.com/watch?v=pSvLCDxvcrU

"Soul Calibur pioneered 8-way running in fighting games"

I gave it credit for that. This affect was already in other kinds of games, including my first one for PSX: WCW vs the World. You could run toward any corner or any rope (8 ways). Applying and enhancing something in other games to a new genre is clever. Definitely changed the dynamics a lot. It wasn't going from Street Fighter or Mortal Kombat to Virtua Fighter or Tekken. Or going from 2D wrestling matches with 4-way movement to WVWvW with 3D graphics and 8-way movement. See the difference?

EDIT: Remembered Ergheiz after I wrote the above. So, maybe Soulcalibur pioneered multi-way movement and maybe other one did. You could run, jump, or fly about anywhere in Ehrgeiz just not as smooth mechanics. Soulcalibur improved on and mainstreamed it either way. Both were published by Namco. So, who knows on that.

"consider the party system in the Street Fighter 3 series (Street Fighter 3: 3rd Strike is the most polished of this series, but the previous two had the same mechanic). This apparently simple change to Street Fighter radically changes the tactics available in game. "

I agree. That's a bigger one. Wrestling games, a variant of fighting games, had Tag Team matches going back to the Wrestlemania games in early 90's. They get the innovation there. It was also a distinctly wrestling concept, too, given you would get a WWF or WCW reply if you said "match where teams fight and you tag them in one at a time" to average person watching TV or playing games. So, you've listed two that came out of 3D and 2D wrestling games respectively.

"I believe Phantasy Star Online was the first ever online console RPG."

Diablo, which it drew on, is the prime innovator in that space. Consoles didn't have internet at all or worth a damn before Dreamcast. Nonetheless, you chose a great example here because nobody believed online RPG's were worth it on consoles. They both delivered one and got console gamers into the online service model. Plus expanded market huge for Diablo-like games into consoles. I give this one credit as a game-changer in its niche. Maybe in industry in general tying in consoles to online services. Baby steps toward Xbox Live and such, wouldn't you say?

"Shenmue and Rez"

Out of time for today given fair videos take time to dig up and watch. ;) They're on my list. I plan to get some vids on Phantasy Star, too, as I forgot the visuals. You got any others you heard were game-changing or way ahead of their time on Dreamcast?