What did the helpless captives from the start of the game do?

At the start of the game

Booker is asked to throw a ball at a tied up couple of a black woman and a white man. However, it's never explained why they are being balled (as in stoned, only with balls). It seems to me, from the set, that they have had interracial relations, but it's never said (at least not to me) that interracial relations are forbidden and not just frowned upon.

Also,

are they supposed to die from the balling as in a real stoning, or just be humiliated?

Solution 1:

It's explicitly because they're an interracial couple.

Remember, the game is set in the early 20th century - such relationships weren't just frowned upon, they were often explicitly illegal. And even when they weren't explicitly illegal, they were generally implicitly illegal, in the sense that people engaged in them would often end up murdered.