How does Redbox keep its supply balanced in each kiosk?

Does Redbox take into account that people are going to return DVDs to different places when they assign certain quantities to each box?

Yes.

Does the number of people renting and returning to different kiosks balance out over time?

Sometimes, but not always.

Do they have to make a run every few days and readjust the numbers, taking some from A and dropping them back off at B and take that surplus to C and so on?

Whether they have to or not depends, but they do stop by every few days and adjust the stock. Even if balance were not an issue, they’d do that at least weekly anyway, to rotate new titles in.

The computer in the machine offers its current supply, whatever that is.

No doubt the machine also reports whenever its supply changes, so they can track what’s where and redistribute the discs as they want.

I have 9 within a 3 mile area. I’m sure it’s not that difficult to restock for them. I do notice however that in heavy snow, they may have a problem with restocking.
But as @zaku points out. It’s directory is probably updated automatically. I know as so as I rent a movie, my husband gets a notice on his phone within minutes.

I would say it’s like all service processing. A router is assigned to a number of kiosks then given a list to replenish on certain days with new disks to include.. they cover their route, maintain a certain number of titles and take out any overs, place the new ones in, take the old ones out and return them to the main center for further processing. A cream job, just hope their paid a fair salary.