TV's do have amplifiers in them. For HMDI signals, they have the digital to analog converter to drive their amplifiers. If you want to obtain the analog audio signal you have to search for a digital to analog converter for HDMI signals that output the HDMI video signal and the analog audio signal.
If you cannot find such a device, then I think you can use an HDMI 1 to 2 splitter to obtain the HDMI signal to feed to your TV for video, and feed the other side to an HDMI to component converter, then feed the audio signals through RCA cables to a stereo amplifier. You may need some RCA to 3.5 mm stereo audio to get the audio from the HDMI to component converter to the device which has the 3.5mm connector.
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