Think of it like this, you have a light switch, you have a light bulb. You can flick the switch as much as you like but if they’re not connected together nothing will happen.
Google Assistant is just the switch, Spotify is the bulb. On your phone the connection is the Spotify app, a Google Home can do the same job. Hope that’s clearer.
Everyone thought releasing the Google Assistant and Alexa SDKs was the path to a free/cheap Home or Echo, unsurprisingly Amazon and Google aren’t that stupid.