Is there a specific term for "conditions treated as though there are OR operators between them"?
I would simply write it in plain English, with any: “the program will exit if any of the three conditions is triggered”.
Usually the way this is written is to list the conditions that trigger an event, and add "whichever comes first":
The game ends when all other players go bankrupt, one player reaches $1,000, or the time limit has been reached, whichever comes first.