All the processing happens on their servers so your computer isn't taxed at all. Been running all sorts of games on my 2015 MBP without any issues -no increased temperatures, no loud fans etc.
I've been amazed by Stadia. As long as you have a fast internet connection, it's pretty a pretty amazing gaming experience.
EDIT: I'm certainly not getting 60 fps even with 1g fiber, but I'm gaming on a 2015 MBP.