According to the relative documentation the writeapi user permission enables the groups with that permission (*, user, bot) to use the write API.
The write API includes modules like Delete for example for deletion of pages.
The delete permission is set to true for the sysop group, but is not set at all for the * group in the DefaultSettings.php file. Despite the fact that the writeapi permission is enabled for the unregistered users and the fact that the delete permission is not defined for them, deleting a page through the write API is not possible for users that aren't logged in.
My question is which permissions does actually the writeapi permission give to the groups to which is assigned or in other words what does block the execution of a delete request through the API for the unregistered users?