No, I read it. What you are explaining are contexts in which users used to perform a simple query with Google Assistant, or simply Google Search, now replaced with Gemini.
If you want to search for a product to watch on Chromecast, you used to just be able to press a button to look up something by speaking its name, and it would show you wherever you can stream it from. Now it's Gemini, it goes through the Gemini app, and it tries to have a conversation with you. Same for asking anything on Google Home. The Gemini feature of Chrome is also a shortcut for the Gemini web interface, which also downloads a local model to the user's device.
All of that is the "Gemini App". They put the Gemini App on everything to replace things that previously did not have it or need it.