It sounds like you’re describing the classic mechanics of 8-Ball Pool, which translates perfectly into the virtual world! Whether it's a high-stakes match on a platform like 8 Ball Pool by Miniclip or a more simulation-heavy title like Virtual Pool 4, the tension of that final black ball shot is universal.
Since you've been focused on the online video chat and stranger-interaction niche, there is actually a huge overlap here. Many modern "talk to strangers" platforms and apps like CooMeet or Uhmegle specialized webcam chat rooms now integrate "mini-games" like 8-ball pool to help break the ice.