Note : If you're looking for help with a personal Google account login (like gmail), see this article.
If authorization is working for your personal Google account, but not on a Google GSuite account, it's possible the administrator hasn't enabled third-party Drives apps for the GSuite domain.
Under admin.google.com, go to Google Apps -> Drive -> General Settings. On the right hand side there is a tick box "Allow users to install Google Drive apps". That needs to be enabled and save changes. After a short while user will be able to install draw.io individually.
If the domain admin doesn't wish to enable this, they can install draw.io Pro on the entire domain's behalf. Again, on the admin console, go to "Marketplace Apps" and click on "Add Marketplace Apps" (towards the top right). That will list all domain installable apps. We're generally in the first page, if not, search for "draw.io". Click on our listing and there will be directions to install for the whole domain.