Even for Microsoft Windows users, S3 graphics cards remain quite rare these days on modern systems. S3 Graphics still has the Chrome 500/400 series as well as the Chrome 20 series, but they are hard to find in new PCs and it can be difficult to still even find them for sale. For a brief time, S3 Graphics on Linux looked a bit interesting when they were advertising a magical GPU Linux driver that offered Blu-ray support, DirectX 10.1, OpenGL 3.0, and NVIDIA VDPAU support under Linux. They were working on a new Linux driver and it did indeed comply with OpenGL 3.0~3.1 on supported hardware and supported NVIDIA's VDPAU API for hardware-accelerated video decoding.
They did release a few Linux GPU driver updates but nothing got better from there. The company's latest Linux driver for 32-bit and 64-bit platforms is version 14.05.02, which made its debut in September of 2011. This driver update simply offered up bug-fixes. Since last September, S3 has updated their Windows XP, Vista, and 7 drivers, but the Linux driver hasn't seen any new release.
With the unstable API/ABI for the X.Org Server and Linux kernel, this S3 binary driver from 2011 will certainly not work on any modern Linux desktop installation using the newer kernel/xorg-server.
Aside from the binary blob, there isn't any proper open-source S3 Graphics driver for their modern Chrome graphics adapters. Like the VIA hardware, you should avoid S3 Graphics if you are a Linux user since their driver support is now even worse off. The latest S3 Graphics products also aren't anything compelling at the hardware level compared to modern Intel/AMD/NVIDIA GPUs where you will find much better Linux performance and support.