In To Kill a Mockingbird, when Atticus asks the children if their game pertains to the Radleys, Jem says, “No sir.” Atticus merely responds, “I hope it doesn't.” Why does he stop the conversation at that point?

Atticus is a thoughtful and involved parent, so he probably has a couple of reasons for not continuing in this conversation.
First, he knows that the kids are lying. When questioned, Jem cannot even come up with an explanation for what they are doing, providing only a vague, "Nothing," in response to his father's questions.
Second, engaging his children in an argument outside would likely attract the attention of the neighbors, and the children have already noted Miss Maudie staring at them from across the street with "her hedge clippers poised in midair." It's a reasonable assumption that Miss Maudie has given Atticus the heads-up about this little game since they are friends, and the children do not even notice Atticus on this day as he stops to watch them. And the Radley house is close by, so Atticus surely doesn't want this argument played out right in front of them.
Atticus likely also wants the kids to come to their own conclusions about why this is the wrong thing to do. Scout really doesn't want to play anymore, anyway, because she has heard someone inside the Radley house laughing at them. Instead of a lengthy talk about how wrong it is to make fun of someone else, Atticus plants a seed in the minds of his children and leaves them to personally reflect on their actions, a more powerful means of corrective behavior than simply being an authoritative parent.