Why do some apps not have to ask for the "Draw over other apps" permission?
Based on an answer by Mattia Maestrini on Stack Overflow,

It is a new behaviour introduced in Marshmallow 6.0.1.
Every app that requests the SYSTEM_ALERT_WINDOW permission and that is installed through the Play Store (version 6.0.5 or higher is required), will have granted the permission automatically.
If instead the app is sideloaded, the permission is not automatically granted. You can try to download and install the Evernote APK from apkmirror.com. As you can see you need to manually grant the permission in Settings -&gt; Apps -&gt; Draw over other apps.
These are the commits [1] [2] that allow the Play Store to give the automatic grant of the SYSTEM_ALERT_WINDOW permission.