I do kinda wonder if that TRex demo is baked on a SGI workstation, honestly. I can hardly see any pixelization in that demo video, and that's a sign right there that it might not be PS1 hardware at all. That video also looks to have some model skin animation going on. Did PS1 really do that, especially early on? That there is absolutely no detail other than the dino though could mean it is some ultra-tweaked code pulling that off.
I don't remember those years as really being "defined" by PS1 hype, honestly. Sony was totally unknown and not really respected before PS1 established itself. I was firmly entrenched in PC and some N64 hype, along with SNES still. And honestly, once I was used to playing N64 and having Voodoo Graphics on PC, PS1 was just painful to look at with its horrible perspective errors and pixelization. Nowadays, IMO, PS1 has lots of overly rozy warm fuzzy memories associated with it.
But I don't think PS1 was any kind of grand super overachiever in moving the industry forward. PC and 3DO were doing that just fine. Doom and Wolf3D were obviously massively popular, even if they weren't true 3D. They built up the buzz. FMV too was just building up its years of grand popularity. FMV 3D too was still mis-understood in comparison with realtime 3D.
3DO, while an expensive failure, was seen as a sort of weird luxury console with mysterious 3D capabilities (lots of it FMV too, obviously). Even SNES and Genesis took a swing at 3D imagery with games like Donkey Kong Country, StarFox, using the carts with 3D processors. Donkey Kong Country basically defined consoles for 1994. Nintendo called it "the year of the cartridge", I believe, snubbing the goofy "32-bit" machines. And Sega was just pumping out 3D hardware like crazy and had tons of Saturn/Neptune/etc hype flying around.
I always felt that PS1 was a sort of a combo "light" 3D device with a major focus on FMV as well. I was more fascinated by N64 and M2, by far.