Mostly affects UK, Germany, Russia and Poland users. https://www.theguardian.com/media/pda/2010/may/04/digital-media-google

So I've recently had issues with logging into games and apps on my phone and today I finally fixed it!

There is an issue with a login API that doesn't support the @googlemail emails anymore, causing failed logins. This affects any app that requires or utilises your Google account login. @googlemail accounts are older alternative gmail accounts (>5 years?) used in countries where the @gmail name was trademarked. @googlemail and @gmail can be used interchangeably for emails, however it may cause login issues for Android apps.

Steps to fix

• go to https://mail.google.com/mail/u/0/#settings/accounts
• under Send mail as, press the link to switch your @googlemail.com to a @gmail account.

When I did this, I had to relogin on my phone and it started working again!

Edit: Added some more details.