@Dorianwalk
You got good info above, and I just want to add a little more: I bought one of the original Dots, specifically so I could add it to my stereo system. You will need to add the audio output of the Dot to a high level input of the stereo using the cables you describe. A high level input such as AUX in is perfect, unless, you like me have run out of high level inputs, then you will need to sacrifice one. I had audio out from my iPod plugged into Tape 1 input, but I had to disconnect it so I could plug in the Dot output.
You have to switch between source inputs of your amp switch to play the Dot sound through the amp (this goes for any source input). I have a lot of audio sources, so it is often a task to remember which is which!
One thing you can do, though, is even when the Dot is connected to the stereo, I can also send Dot output to Bluetooth speakers (e.g. a portable stereo one) and still use the amp for other sources. That way you can use the Dot for Alexa use and play some other audio out of the stereo. You just can't do both at the same time with Dot. I have done this to see that it can be done; I do not do this as a regular thing. But, it can be done. Example: I want to watch a sport event on TV with its sound through stereo, but still use Dot's Alexa during the game. I have an Echo nearby and another Dot, so I really don't need to do this. But, if I didn't, I could use the Dot on the stereo this way. In actuality, once a Dot is connected to stereo, there are limitations on using the Dot for Alexa all the time.