The GeForce 9xxx series didn't have HDMI audio controllers on the GPU. That is why you don't see any HDMI audio devices.
In Stephen's GPU HDMI Audio Document, this is what is referred to in section 3.1 as "Pre-Azalia":
Some older GPUs included a connector to receive S/PDIF audio from a separate sound card, and route that audio over HDMI. This document does not cover such devices at all.
Look for a 3-pin header on your GPU board near the HDMI port. Usually it's labeled "SPDIF IN". You will need to connect this header to some SPDIF output on some sound controller, since the GPU doesn't have a sound controller of its own. It is this sound controller that you will be driving via ALSA.
Once you have the header connected, audio playing over that SPDIF output will be passed through to the HDMI port.