Comment # 4 on bug 1172498 from Takashi Iwai

Are you sure that you had an HDMI audio output from Nvidia graphics?
Yours looks like a hybrid graphics, i.e. the all mode set is done on Intel
graphics side while Nvidia chip does 3D rendering.  In that case, usually the
whole HDMI audio is managed in Intel graphics, i.e. it's via Intel PCH.

The alsa-info.sh output indicates that HDMI audio devices are registered.
And HDMI should be available on PulseAudio output, too.
(Though, the connection state is negative; you took alsa-info.sh while not
connecting to an HDMI monitor?)