The Stadia controller should have gyroscope to aim:
https://www.youtube.com/watch?v=3X1pd4UzubQ
the mouse of the desktop version could be simulated by the gyro when the person presses the button to aim (configuration disabled or enabled in the game or in the Stadia system) and may have other interactions besides this
if you don't have it today, in the future you have to have a version with Gyroscope
That's an interesting idea. Please be sure to use the Feedback option in the Stadia app to suggest it directly to the Stadia development team.