As it seems right now, it is only possible to play Google Stadium if you have a Wi-Fi nearby. This will change soon.
Now it has emerged that Google is working on a "new" feature for Google Stadium that will allow you to play either over Wi-Fi as it looks right now or via mobile data. On the other hand, you can expect to learn a lot of data if you choose to play over this.
It is currently unclear when Google will begin this feature but hopefully it will be within card.