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Ok, your laptop has an internal Realtek audio solution that is capable of outputting to the external headphone connector. Is this not what you want?
If the connected HDMI device does not have an audio output capability, the Intel HD Audio driver is not going to assert itself and take over from the audio output path.
When the TV is enumerated, the Intel HD Graphics driver is supposed to recognize that an audio output capability is present (by interrogating the EDID data from the TV) and should automatically override and enable the Intel Display Audio driver as being the current audio output path. I do not understand why this is not working. Intel Customer Support is going to have to take over this investigation.