System admin logged in as 'Standard User' can still access the Developer Console

By default, Standard profile users do not have the "View All" and "Author Apex" perms and so, they do not have access to Developer Console. However, when a System admin logs in as Standard profile user (via Login As functionality ), can access the developer console.

Note: As an Admin who has these permission, logging into a user using granted login access will allow you to see this option under the drop down. Even though you as the system admin can see it, if the user does not have "View  All Data" and "Author Apex" permissions, they will not be able to see it via normal login. 

Enable the 'Administrators can login as any User' feature