Stack Exchange already uses the OAuth 2.0 APIs to log you using a Google account; note the URL in those screenshots. You can also verify this by logging in with a Google account, the login screen URL contains:
As such, Stack Exchange is not affected by this deprecation, it is already using one of the recommended APIs.
However, StackExchange.com, the Data Explorer, and Area 51 have not yet been updated; you will see the deprecation warning there if you use Google to log in. The Data Explorer is Open Source, so if you can help out with migrating that stack, please do so! It'll be interesting to see if Area 51 will get the update any time soon; the stack running that site is quite outdated.