Only
Team Members can be selected to own artifacts. That is the behavior not only for Kanban Board but for any app and also for the product screens. Even a Subscription Administrator can not be made owner unless is added to the team.
Here is a similar example not out of the Kanban Board but from the User Story detail page. It shows the same selection options:
<Please see attached file for image>

As said, in order to allow users to own artifacts they must become Team Members. This includes any user, even the sub-admins.
To learn more on how to make users become
Team Members, see:
https://help.rallydev.com/administer-users#permissions
<Please see attached file for image>

Also, see:
https://help.rallydev.com/setting-projects