Do I Need To Add The Business Owner As A Partner?

Hi,

No. This option is there for when you have the option "Add partner to user account during registration" activated so that when a user registers, his affiliate partner is linked to his account so that future orders will be linked to that affiliate partner.
So for user accounts of affiliate partners like the one on your screenshot, you don't want to select anything in there or maybe himself if you want that his own orders get assigned to himself with the "No self affiliation" setting activated.