I received something similar from Gmail when trying to use my account.
Someone just tried to sign in to your Google Account XXXX@gmail.com from an app that doesn't meet modern security standards.
Details:
Sunday, August 23, 2015 11:01 AM (Eastern Daylight Time)
Ashburn, VA, USA*
We strongly recommend that you use a secure app, like Gmail, to access your account. All apps made by Google meet these security standards. Using a less secure app, on the other hand, could leave your account vulnerable. Learn more.Google stopped this sign-in attempt, but you should review your recently used devices:
I assume this is the webserver and I allowed Google to recognize it as one of my devices but the WP Mail SMTP plugin is still reporting that it can't authenticate me.
I started to look into this because I didn't really like how my gmail password was just sitting unobscured in the dashboard and eventually found the Postman plugin which uses OAuth2.0 and while somewhat tricky to set up eventually gets you an authorized google app that sends email.