Most sound cards produced in 1998 and later would have hardware mixing. The first I remember is the Diamond Monster Sound MX200/M80 with the Analog Devices chipset with DSP based Aureal A3D. That is actually a 1997 card.
Aureal then built their Vortex ASICs. I don't think Vortex Advantage is hardware accelerated but Vortex 1 and 2 are.
Live is Creative's first card. The cards that use AudioPCI chips are software. So are motherboard integrated and USB chips.
ESS Maestro and later PCI chips.
Philips / VLSI Thunderbird.
Crystal CS46XX.
CMedia CMI 8738.
Few motherboard solutions are hardware except the CMedia 8738.
This is just from memory.
The Win9x DirectX sound acceleration slider lets you control how directly Windows uses the sound card's driver's features or bypasses all of it. The driver can implement its own processing that appears as hardware mixing to the OS.
On the WAV API output, at least the Live can play more simultaneously even with VXD. It has a control panel applet to set the limit.