The point is to set up a smartthings routine which causes a voice assistant to speak a custom phrase. Then a different Google device would hear that custom phrase and do whatever you wanted it to do.
This is very easy with echo, because The standard Alexa routines (no raspberry pi or AskAlexa required) let you trigger a custom phrase from a sensor. So you can use a virtual sensor in SmartThings and use that to trigger the Alexa routine. I Already mentioned this above.
FAQ: Can I trigger an Echo Action without Speaking to It?
If you don’t want to use an echo device, you can do the same thing with an android device and LANnouncer, although that’s quite a bit more work.