Google owns the .google gTLD but they haven't been using it for any of their existing products. So far blog.google is the most used. Why haven't they moved * .google.com to * .google?
Gmail (mail.google.com) to mail.google, docs.google.com to docs.google and so on.
Browser support in 2018 should have caught up to support them.
I'd at least expect them to redirect mail.google to mail.google.com if they plan to keep the existing domains.