It seems that your post contains the answer. The account that you were trying to use has some features limited and these features are required by Google Arcade game. I am not familiar with the game’s internals and concluding it based on the info you shared.
Try to use your personal gmail account or create a new one. This should be OK to play the game. If it is a part of the student experience, I would recommend to contact an authority that provided you with this account and ask them to validate the account configurations.