rollotomasty :
I thought this might be the case. However, a game I'm interested in, The Vanishing of Ethan Carter, says it requires the sound to be DX9c. Since I don't have a dedicated sound card, I'd have to use the sound from my graphics card's HDMI I guess? My speakers are old and I don't have a monitor passthrough :/
That's the responsibility of the operating system and sound card driver, not the sound card itself.
Unlike the graphical subsystem, explicit hardware acceleration of audio on Windows is extremely limited. The choice of how to perform most of the operations is left up to the sound card driver. There is a uniform software interface between the windows audio service and the device driver, but the application side is purely virtual. Hardware specific features such as EAX can only be accessed through third party libraries such as OpenAL (note that EAX used to be accessible through DirectX, but no longer).