So your checkmk agent runs as user cmkadmin and your MySQL instance only allows access for user root?
Then I’d suggest you create a user whithin MySQL (can be cmkadmin or some other monitoring user) and configure a password for that user. The manual explains this quite good.
Then configure that very same user and password in mysql.cfg.
The !include is only neccessary if you deploy the file via the Bakery and want to overwrite or add some settings locally on the machine.
About the socket I’m not sure. Maybe the value shown is the default value anyways.