Why can a Space Admin not manage other people's rules?
Because the role takes two grants and neither works on its own.
The person must administer the space in Jira, under Space settings > Access, and that space must also be selected in the app under App Settings > Permissions > Space Admins.
Owning the space is not a substitute for either.
Related pages
Permissions and Access Requirements - where this is covered in full.
User Permissions - more questions on this topic.