The first 3D I remember having played was Major Havoc or I robot - so yes there were "real" 3D games in the market, but 3D completly took over the home market, except handheld like the Gameboy/Advanced/DS/... (I think the 2D revival came with the indy developer movement, but I'm not sure).
Also see e.G. the transition from Bards Tale 3D (small window) to Dungeon Master 3D (main window, 3D interaction) and then Ultima Underworld 3D (all in, tilt, up/down) as an example of 3Dification of games and genres.
Sega released Saturn as a full fledged, 3D focused hardware. A year before the PlayStation 1 was out.
Some chronological refresher:
Sega had already been successful in making arcade 3D games and were the first to effectively transition true 3D to the home markets with multiple early flagship releases such as Virtual Fighter, beautifully ported to the home console.
The reason not many decent 3D games were shipped on Saturn was not down to the hardware capabilities or goal from sega to embrace expected 3D market demands. It was rather due to the horrific developer experience. It was so terribly difficult to program it, only those at sega were comfortable with it, if that.
Saturn's hardware architecture complexity, having multiple CPUs, and other design aspects prove bad choice as it jeopardised 3rd party game developers productivity. Words were that most games shipped leveraging a single CPU given how obscure dual cpu programming was.
Ironically Sega designed a more powerful machine than the PS1 and got it out a whole year earlier, yet games on PS1 were significantly superior. All down to ease of development.
Wipeout was an early game on PS1 and indeed among many other popular games sealed the fact home gaming would be 3D. But sega had already produced a full fledged 3D capable Saturn, they didn't wait to see wipeout in 1995/1996, or Mario 64 another 2 years later. Saturn was capable of running wipeout 2097, metal gear solid, grand tourismo, and other late PS1 games that pushed the ps1 to its limits. But it missed the momentum and studios were not anymore invested in the saturn. Its marketshare kept shrinking.
what the Dreamcast got added was primarily developer friendly features, the rest was simply leaps forward in compute power, especially on the GPU. Bump mapping if I'm not mistaken was supported by the Dreamcast first among home consoles. It was not "added" 3D, for sega that was its 2nd generation of 3D focused hardware, also their 2nd attempt, both ultimately failed for different reasons.
If you'd implemented a z-Buffer in software you could sort these sprites to draw them in the right sequence to use the distorted sprites as 4-corner polygons to render 3d models.
The Dreamcast added a 3D GPU with the PowerVR2.
[0] https://www.copetti.org/writings/consoles/sega-saturn/#graph...
VDP1 draws distorted textured quads (it's misleading to call them sprites). The playstation's GPU displays distorted textured triangles.
The playstation GPU also knows nothing about 3D, it doesn't have a depth buffer. Like the Saturn, you have to implement depth sorting on the CPU and link all those distorted triangles up in the right sequence of 3-corner polygons to render a 3D model.
Yet nobody ever claims the playstation isn't a 3D console.
"Sega calls them ‘distorted sprites’" [0]
[0] https://www.copetti.org/writings/consoles/sega-saturn/#graph...
And if you are in a discussion about if VDP1 is 3D capable or just advanced 2D hardware that clever programmers tricked into doing 3D, then it doesn't really matter what terminology Sega used.
It's misleading terminology because if the person you are talking to doesn't understand the functional equivalence between distorted sprites and texture-mapped quads, as the "sprite" terminology might lead them to assume it's 2D-only hardware.
This was not the discussion. The discussion was if Sega missed the total shift of gaming to 3D games that was brought on by 3D graphics cards and that propelled PCs into the mass gaming market (before 3D it mostly excelled at thing consoles couldn't do, like text adventures and point&click). And that it didn't need 2D hardware (at least for the international market, JP had e.G. more Shmups and it seems less interest in 3D shooters) but dedicated 3D hardware like the PowerVR2 they did put in the Dreamcast (too late, and I wrote Dreamcast software and loved the machine, so I'm not against Sega hardware in any way). And if they had anticipated the move of games (the vast majority of todays AAA titles are 3D games, for the better or worse, and in the Top 10 of most sold games, 8 are 3D and 2 are 2D or 2.5D) in it's majority to 3D, they at least had a chance to overtake the Playstation and survive as a game hardware vendor. The Saturn was only on par with the Playstation (e.G. at the time I owned Tomb Raider on both), which wasn't enough.
If you take a look at the most sold PS1 games, it's mostly 3D games:
https://en.wikipedia.org/wiki/List_of_best-selling_PlayStati...
The Wikipedia page says this about 3D of the Saturn:
"[..] which resulted in the creation of the "SuperH RISC Engine" (or SH-2) later that year [..] According to Kazuhiro Hamada, [..] we realized that a single CPU would not be enough to calculate a 3D world." Although the Saturn's design was largely finished before the end of 1993, reports in early 1994 of the technical capabilities of Sony's upcoming PlayStation console prompted Sega to include another video display processor (VDP) to improve 2D performance and 3D texture mapping"
Sega build the Saturn without a focus on 3D. Because they saw 3D coming too late, late in and after development had mainly finished, they added a 2nd CPU and added a VDP for 3D texture mapping to compensate for the lack of 3D capabilities.
The Saturn only beat the playstation to the Japanese market by 11 days.
The gap was more like 3 months in other markets, but only because Sega bought the launch date forwards (with disastrous results. In North America it was scheduled to launch one week before the Playstation, but Sega said "Surprise, it's launching today". Many retailers in North America went on to boycott Sega, because they weren't informed about the surprise launch, and didn't have any stock).
Sega's problem wasn't that it didn't see 3D coming. They did, despite the common claims on the internet, the Saturn was designed to be a 3D capable console, with dedicated 3D hardware.
Sega's problem is that they bet on the wrong 3D technology. Like Sega's arcade systems. the Saturn was designed for quads, and could only do forwards texture mapping (which doesn't allow for UV coordinates).
While the playstation went for triangles and inverse texture mapping. It turns out that was the correct direction, and the whole industry settled on that as a standard. All game engines and tooling would assume triangles.
To make things worse, the Sega's hardware 3D implementation wasn't that good even at the techniques it was trying to implement.
"You are forgetting [...] Daytona USA"
Part of the reason why the Saturn port of Dayton USA was so good, is because the game was designed for the Model 2 hardware, and the Saturn's 3D capabilities were cost-optimised versions of the Model 2 3D capabilities.
VDP1 was designed to do 3D. It's not just a 2D sprite engine that developers later tricked into doing 3D, it was absolutely intentional that it would be used for 3D from the very start. the fact the 3D quads could also be used to show thousands of 2D sprites with full scaling/rotation/distorting was more of a intentional bonus of the design.
Yes, Sega did miss a trick by also dedicated a bunch of the silicon budget to 2D-only capabilities. VDP2's four layers of scrolling backgrounds plus two layers of mode-7 style "3D planes" are pretty useless for 3D work. They should have dropped VDP2 entirely and and focused on making VDP1 more powerful.
When games were actually designed around the Saturn's 3D capabilities, the results were pretty good. Daytona is great, Tomb Raider is another great.
Some games went further, going out of their way to adjust their game design so they could take advantage of VDP2's 3D planes. That's the major reason why Panzer Dragoon looks so good, the water is a 3D VDP2 layer. The skybox too, but that's reasonably common technique in Saturn games.