S3 predated the GPU wars entirely. Though they did participate with the S3 Virge. Back then everyone had 2D/3D accelerators but really lost out to the VooDoo 1 and later VooDoo 2, which were dedicated 3D cards but were so much faster when utilizing the Glide API. The only thing else like it was the NEC Power VR. For 2D/3D cards you had FireGL, Matrox, ATi, and I think STB had its own or used something from Cirrus Logic, etc.
The only startup I can recall that was poised to take on anyone was ArtX which ATi purchased which led to the creation of the Radeon 9700 Pro. But by then 3DFX was gone and ATi's market share still barely existed. It was Radeon that put them on the map. During those days ATi had its basic bitch 2D chips in every server and workstation and it served as integrated graphics in tons of stuff. All their own 3D accelerators prior to the Radeon series weren't really all that competitive.
There was no "Big 3" by that point. There was NVIDIA, and ATi was just kind of there. I think the "Big 3" that people think of is ATi, 3DFX and NVIDIA but that's not really how it was. Yes they all existed at that time. ATi had volume with ancient 2D only video chips that had a massive OEM presence. In the 3D accelerator world it was always just 3DFX and NVIDIA by the late days of the Riva TNT2 Ultra and the GeForce 256. ATi's Rage Fury Maxx was interesting, but not really all that competitive.
There may have been some startups announced but nothing ever came of any of them.
