No you should not be outputting the audio from your stack amp. lets look at a couple of photos:
Top is your current integrated amp.
Below is an example AVR the Sony 1060.
They are basically the same thing with the the only difference being more inputs and speaker terminals on the bottom unit. Once you have an AVR like the bottom option then all your source devices would be moved out of the denon unit and connected to the new unit. The old stack may have some integrated control between the multiple units which would not work the same once you replace the amp with an AVR and many of the control functions will be done on the AVR with it's remote control now.
The AVR has the addition of video processing via HDMI which means sources like blu-ray players and android/roku/apple_TV streaming devices can plug in and be passed onto the TV and by the AVR. You select which source you want to the AVR remote and its sound gets output via the speakers and video passed onto the TV via HDMI out port.
Now if your only source is the TV itself and its smartTV options and built in TV tuner then the situation is different. In this situation you either use and HDMI cable with a feature called ARC turned on at both AVR and TV end or you get an optical digitial output cable and connect it from the TV to one of the optical inputs on the AVR for it to produce sound in 2 channel or 5.1 from Dolby digital/DTS sources. If this is all you need then getting a new generation latest year model of AVR may be a waste of money as even a 10 year old second hand AVR will do the job just as well and will be cheaper. But if you want to switch multiple 4k HDMI sources then a modern AVR is the way to go.
Note you only have 3 speakers and no sub but these AVR's will still work with this but you may not get surround sound etc.